Professor Emeritus

Department of Mathematics

Interdisciplinary Program in Applied Mathematics

University of Arizona

Tucson, AZ 85721 USA

1. J. M. Cushing, Matrix Models for Population, Disease, and Evolutionary Dynamics, Student Mathematical Library, Volume 106, American Mathematical Society, 2024

2. J. M. Cushing, Shandelle M. Henson, and James L. Hayward, Modeling Behavior and Population Dynamics: Seabirds, Seals, and Marine Iguanas, Interdisciplinary Applied Mathematics, Volume 57, Springer Nature, Switzerland, 2023

3. J. M. Cushing, R. F. Costantino, Brian Dennis, Robert A. Desharnais, and Shandelle M. Henson, Chaos in Ecology: Experimental Nonlinear Dynamics, Theoretical Ecology Series, Volume 1, Academic Press (Elsevier Science), New York, 2003, ISBN: 0-12-1988767

“In
terms of what they
reveal about the mechanisms of population growth, about nonlinear
stage-structured population models, and about chaos in ecology, these
experiments are on the level of the classic works of Gause, Nicholson,
Park, and Huffaker. In terms of the integration of experiment
and
theory, they surpass even those studies. Anyone interested in the
dynamics of populations will benefit from reading this book."
--
Hal Caswell, Ecology
(2003)

“This is the definitive source on chaos in ecology. Well-written and authoritative. ” -- Simon Levin, Princeton University 2002

“The authors have made very circumspect model verifications...The greatest merit of the book is that it confirms experimentally the existence of numerous nonlinear phenomena in populations and presents a new characteristic of populations, that is, the lattice effect. The book is written in an excellent style with high mathematical precision. This work is warmly recommended to all theoretical and field ecologists, and all scientists interested in nonlinear dynamics.” -- Community Ecology (2005)

“... rich in statistical concepts and methods. Anyone interested in the dynamics of populations will benefit from reading this book.” -- Ecology (2003)

“... an elegant blend of mathematics, statistics, and biology...” -- Chance (Fall 2003)

“Chaos in Ecology ought to be read by both field and theoretical ecologists.” -- Complex Systems Lab, Barcelona, Spain (2002)

4. J. M. Cushing, An*Introduction
to Structured
Population Dynamics*,
Conference Series in Applied Mathematics
Vol. 71, SIAM, Philadelphia, 1998, ISBN 0-89871-417-6 ERRATA

5. J. M. Cushing, Integrodifferential Equations and Delay Models in Population Dynamics, Lecture Notes in Biomathematics 20, Springer, Berlin Heidelberg New York, originally published in 1977 and reprinted in 2013, ISBN 978-3-642-93073-7.

6. J. M. Cushing, Differential Equations: An Applied Approach, Pearson - Prentice Hall, Upper Saddle River, New Jersey 2004, ISBN: 0-13-044930-X.

## BOOKS IN PREPARTION

## BOOKS
EDITED

## JOURNAL ARTICLES

J. M. Cushing / Department of Mathematics / Program in Applied Mathematics / University of Arizona / Tucson, AZ 85721-0089

(revised 29 February 2024)

© Copyright 2000-2025 Jim M Cushing

All rights reserved

“This is the definitive source on chaos in ecology. Well-written and authoritative. ” -- Simon Levin, Princeton University 2002

“The authors have made very circumspect model verifications...The greatest merit of the book is that it confirms experimentally the existence of numerous nonlinear phenomena in populations and presents a new characteristic of populations, that is, the lattice effect. The book is written in an excellent style with high mathematical precision. This work is warmly recommended to all theoretical and field ecologists, and all scientists interested in nonlinear dynamics.” -- Community Ecology (2005)

“... rich in statistical concepts and methods. Anyone interested in the dynamics of populations will benefit from reading this book.” -- Ecology (2003)

“... an elegant blend of mathematics, statistics, and biology...” -- Chance (Fall 2003)

“Chaos in Ecology ought to be read by both field and theoretical ecologists.” -- Complex Systems Lab, Barcelona, Spain (2002)

4. J. M. Cushing, An

5. J. M. Cushing, Integrodifferential Equations and Delay Models in Population Dynamics, Lecture Notes in Biomathematics 20, Springer, Berlin Heidelberg New York, originally published in 1977 and reprinted in 2013, ISBN 978-3-642-93073-7.

6. J. M. Cushing, Differential Equations: An Applied Approach, Pearson - Prentice Hall, Upper Saddle River, New Jersey 2004, ISBN: 0-13-044930-X.

- Shandelle M. Henson, Robert A. Desharnais, R. F. Costantino, J. M. Cushing, and Brian Dennis, Nonlinear Patterns in Population Dynamics: Theory and Experiments, Chapman & Hall/CRC
- Saber Elaydi and J. M. Cushing, Discrete Mathematical Models in Population Biology: Ecological, Epidemic, and Evolutionary Dynamics, Springer-Verlag

- Soring Olaru, Jim. Cushing, Saber Elaydi, René Lozi, Difference Equations, Discrete Dynamical Systems and Applications, IDCEA 2022, Gif-sur-Yvette, France, June 18–22, Springer Proceedings in Mathematics & Statistics, Volume 444, Springer Cham, 2024
- J. M. Cushing, M. Saleem, H. M. Srivastava, M. A. Kahn, and M. Merajuddin, Applied Analysis in Biological and Physical Sciences, Springer Proceedings in Mathematics & Statistics, Volume 186, Springer, India, 2016
- Lluis Alseda Soler, Jim M. Cushing, Saber Elaydi, and
Alberto Adrego Pinto, Difference
Equations, Discrete Dynamical Systems and Applications, Volume
180, Springer Proceedings in Mathematics & Statistics,
Springer, Berlin & Heidelberg, 2016

- Ziyad AlSharawi, J. M. Cushing, and Saber Elaydi, Theory and Applications of Difference Equations and Discrete Dynamical Systems, Springer Proceedings in Mathematics & Statistics, Vol. 102, Springer, Heidelberg, 2014
- S. Elaydi, J. M. Cushing, R. Lasser, V. Papageorgiou, A. Ruffing, W. Van Assche, Difference Equations, Special Functions and Orthogonal Polynomials, World Scientific Publishing Co. Pte. Ltd., Singapore, 2007

- J. M. Cushing, Junpyo Park, Alex Farrell and Nakul Chitnis, Treatment outcome in an SI model with evolutionary resistance: a Darwinian model for the evolution of resistance, Journal of Biological Dynamics, 17:1, (2023), DOI: 10.1080/17513758.2023.2255061
- J. M. Cushing and Kathryn Stefanko, A Darwinian dynamic model for the evolution of post-reproduction survival, Journal of Biological Systems 29(2) (2021), 433-450, https://doi.org/10.1142/S0218339021400088
- J. M. Cushing, A bifurcation theorem for Darwinian matrix models with an application to the evolution of reproductive life history strategies, Journal of Biological Dynamics 15:sup1 (2021), S190-S213, https://doi.org/10.1080/17513758.2020.1858196
- J. M. Cushing, A Darwinian Ricker equation, Progress on Difference Equations and Discrete Dynamical Systems (S. Baigent, M. Bohner, S. Elaydi, editors), Springer Proc. Math. Stat., vol. 341, Springer, Cham, [2020] ©2020, pp. 231–243, DOI 10.1007/978-3-030-60107-2_10. MR4219152
- J. M. Cushing and A. P. Farrell, A
bifurcation theorem for nonlinear matrix models of population dynamics,
Journal of
Difference Equations and Applications 26(1) (2020), 25-44, http://dx.doi.org/10.1080/
10236198.2019.1699916 . - J. M. Cushing, Discrete time Darwinian dynamics and semelparity versus iteroparity, Mathematical Biosciences and Engineering, 16(4) (2019), 1815-1835, DOI 10.3934/mbe.2019088
- J. M. Cushing, Stability and the geometry of bifurcation graphs for a class of nonlinear Leslie models, Difference Equations and Discrete Dynamical Systems with Applications, Proceedings in Mathematics & Statistics (M. Bohner, S. Siegmund, R. Hilscher and P. Stehlik, eds.), Springer Nature Switzerland, 2019, pp. 201-211
- J. M. Cushing, Difference Equations as Models of Evolutionary Population Dynamics, Journal of Biological Dynamics 13 (2019), 103-127, DOI 10.1080/17513758.2019.1574034
- J. M. Cushing and S. M. Henson, Periodic matrix models for seasonal dynamics of structured populations with application to a seabird population, Journal of Mathematical Biology 77 (2018), 1689-1720, DOI: 10.1007/s00285-018-1211-4
- S. L. Robertson, S. M. Henson, T. Robertson and J. M. Cushing, A matter of maturity: to delay or not to delay? Continuous-time compartmental models of structured populations in the literature 2000-2016, Natural Resource Modeling 31, No. 1 (2018), 1-26, DOI: 10.1111/nrm.12160
- J. M. Cushing, F. Martins, A. A. Pinto, A. Veprauskas, A bifurcation theorem for evolutionary matrix models with multiple traits, Journal of Mathematical Biology 75, No. 1 (2017), 491-520, DOI: 10.1007/s00285-016-1091-4
- P. De Leenheer, A. Mohapatra, H. A. Ohms, D. A. Lytle, and J. M. Cushing, The puzzle of partial migration: adaptive dynamics and evolutionary game theory perspectives, Journal of Theoretical Biology, 412 (2017), 172-185, DOI.org/10.1016/j.jtbi.2016.10.011
- A. Veprauskas and J. M. Cushing, A juvenile-adult population model: climate change, cannibalism, reproductive synchrony, and strong Allee effects, Journal of Biological Dynamics 11, Sup1 (2017), 1-24, DOI: 10.1080/17513758.2015.1131853
- J.
M. Cushing and O.
Diekmann, The
many guises of R
_{0}(a didactic note), Journal of Theoretical Biology 404 (2016), 295-302, DOI:10.1016/j.jtbi.2016.06.017 - E. P. Meissen, K. R. Salau, and J. M. Cushing, A global bifurcation theorem for Darwinian matrix models, Journal of Difference Equations and Applications 22, No. 8 (2016), 1114-1136, DOI 10.1080/10236198.2016.1177522
- J. M. Cushing, One dimensional maps as population and evolutionary dynamic models, Applied Analysis in Biological and Physical Sciences, Springer Proceedings in Mathematics & Statistics, Volume 186, (J. M. Cushing, M. Saleem, H. M. Srivastava, M. A. Khan, M. Merajuddin, eds.), Springer, India, 2016.
- Shandelle Henson, J. M. Cushing and James Hayward, Modeling animal behavior in a changing environment, Resource Modeling Association Newsletter, Spring 2016
- A. Veprauskas and J. M. Cushing, Evolutionary dynamics of a multi-trait semelparous model, Discrete and Continuous Dynamical Systems Series B 21, No. 2 (2016), 655-676, DOI:10.3934/dcdsb.2016.21.655, errata
- A. S. Ackleh, J. M. Cushing, and P. L. Salceanu, On the dynamics of evolutionary competition models, Natural Resource Modeling 28, No. 4 (2015), 380–397, DOI: 10.1111/nrm.12074
- J. M. Cushing, S. M. Henson and J. L. Hayward, An evolutionary game theoretic model of cannibalism, Natural Resource Modeling 28, No. 4 (2015), 497–521, DOI: 10.1111/nrm.12079
- J. M. Cushing, The evolutionary dynamics of a population model with a strong Allee effect, Mathematical Biosciences and Engineering 12, No. 4 (2015), 643-660
- J. M. Cushing, On the Fundamental Bifurcation Theorem for Semelparous Leslie Models, Mathematics of Planet Earth: Dynamics, Games and Science (J. P. Bourguignon, R. Jeltsch, A. Pinto, and M. Viana, editors), CIM Mathematical Sciences Series, Springer, Berlin, 2015, pp. 215-251
- J.
M. Cushing, Backward
bifurcations and
strong Allee effects in matrix models for the dynamics of structured
populations,
*Journal of Biological Dynamics*8 (2014), 57-73 - J. M. Cushing, An evolutionary Beverton-Holt model, Theory and Applications of Difference Equations and Discrete Dynamical Systems (Z. AlSharawi, J. M. Cushing, S. Elaydi, eds.), Springer Proceedings in Mathematics & Statistics, Vol. 102 (2014), Springer, Heidelberg, pp. 127-141
- J.
M. Cushing and Simon Maccracken
Stump, Darwinian
dynamics of a juvenile-adult model,
*Mathematical Biosciences and Engineering*10, No. 4 (2013), 1017-1044

- J.
M. Cushing and S. M. Henson, Stable
bifurcations in nonlinear semelparous Leslie models, Journal
of Biological Dynamics
6
(2012), 80-102

- S.
L. Robertson, J. M. Cushing, and R.
F. Costantino, Life
stage: interactions and spatial patterns, Bulletin
of Mathematical Biology 74
(2012), 491-508

- J.
M. Cushing and Jarred Hudson, Evolutionary
dynamics and strong Allee effects, Journal of Biological
Dynamics
6,
No. 2 (2012), 941-958

- J.
M. Cushing, A
dynamic dichotomy for a system of hierarchical difference equations,
Journal
of Difference Equations
and Applications 18 No. 1
(2012), 1-26

- S. L. Robertson and J. M. Cushing, A bifurcation analysis of stage-structured density dependent integrodifference equations, Journal of Mathematical Analysis and Applications 388 (2012), 490-499
- J. M. Cushing, Difference equations, Encyclopedia of Theoretical Ecology, (A. Hastings and L. Gross, Editors-in-Chief), University of California Press, Berkeley, 2012
- J.
M. Cushing and A. S. Ackleh, A
net
reproduction number for periodic matrix models, Journal
of Biological Dynamics 6,
No. 2
(2012),
166-188

- S. M.
Henson, J. M. Cushing and J. L. Hayward, Socially-induced
ovulation
synchrony
and
its
effect
on seabird populations, Journal
of Biological Dynamics
5, No. 5 (2011), 495-516

- S. L. Robertson and J. M. Cushing, Spatial segregation in stage-structured populations with an application to Tribolium, Journal of Biological Dynamics 5, No. 5 (2011), 398-409
- J. M.
Cushing, On
the
relationship
between r
and R
_{0}and its role in the bifurcation of equilibria of Darwinian matrix models, Journal of Biological Dynamics 5 (2011), 277-297

- R. C. Rael, T. L. Vincent and J. M. Cushing, Competitive outcomes changed by evolution (with errata), Journal of Biological Dynamics 5 (2011), 227-252
- S. M.
Henson, J. L. Hayward, J. M. Cushing, and Joseph G. Galusha, Socially-induced
synchronization of
every-other-day egg laying in a seabird
colony, The
Auk
127, No. 3 (2010), 571-580

- J. M.
Cushing, On
the
dynamics
of
a
class
of
Darwinian matrix models, Nonlinear
Dynamics and Systems Theory
10, No. 2 (2010), 103-116

- J.
M. Cushing, A
bifurcation theorem for Darwinian matrix models,
*Nonlinear Studies*17, No. 1 (2010), 1-13 , errata

- J.
M. Cushing, Matrix
Models
and Population Dynamics, a
chapter in Mathematical
Biology (Mark Lewis,
A.J. Chaplain, James P. Keener, Philip K. Maini eds.), IAS/Park City
Mathematics Series Vol 14, American Mathematical Society, Providence,
RI, 2009, 47-150

- R.
C. Rael, R. F. Costantino, J. M.
Cushing, and T. L. Vincent, Using
stage-structured evolutionary game theory to model the experimentally
observed evolution of a genetic polymorphism,
*Evolutionary Ecology Research*11 (2009), 141-151

- J.
M. Cushing, Three
stage
semelparous Leslie models,
Journal
of Mathematical Biology
59 (2009), 75-104

- S.
L. Arpin and J. M. Cushing, Modeling
frequency-dependent selection with an application to cichlid fish,
*Mathematical Biosciences and Engineering*5, No. 4 (2008), 889-903 - N.
Chitnis, J. M. Hyman and J. M. Cushing, Determining
important
parameters
in
the
spread of malaria through the sensitivity analysis of a mathematical
model,
*Bulletin of Mathematical Biology*70 (2008), 1272-1296 - J.
M. Cushing, S. M. Henson, C. C.
Blackburn, Multiple
mixed-type attractors in competition models, Journal of Biological
Dynamics
1,
No. 4 (2007), 347-362

- S. M. Henson, B. Dennis, J. L. Hayward, J. M. Cushing and J. G. Galusha, Predicting the dynamics of animal behavior in field populations, Animal Behavior 74, No. 1 (2007), 103-110
- R.
C. Rael, T. L. Vincent, R. F.
Costantino and J. M. Cushing, Evolution
of corn oil sensitivity in the flour beetle,
*Advances in Dynamic Game Theory*, Jørgensen, Quincampoix and Vincent, eds., Birkhäuser, Berlin, 2007, pp. 367-376 - S.
M. Henson, J. G. Galusha, J. L.
Hayward and J. M. Cushing, Modeling
territory attendance and preening behavior in a seabird colony as
functions of environmental conditions, Journal
of Biological Dynamics 1,
No. 1 (2007), 95-107

- J. M. Cushing, S. M. Henson and Lih-Ing Roeger, A competition model for species with juvenile-adult life cycle stages, Journal of Biological Dynamics 1, No. 2 (2007), 201-231
- J. M. Cushing, Nonlinearity and stochasticity in population dynamics, Mathematics for Ecology and Environmental Sciences, Volume 1, (Takeuchi, Iwasa, and Sato, eds.), Springer, Berlin, 2007
- N. Chitnis, J. M. Cushing and J. M. Hyman, Bifurcation analysis of a mathematical model for malaria transmission, SIAM Journal on Applied Mathematics 67, No. 1 (2006), 24-45
- J.
M. Cushing, A
juvenile-adult model with periodic vital rates, Journal
of Mathematical Biology
53 (2006), 520-539

- R. A. Desharnais, R. F. Costantino, J. M. Cushing, S. M. Henson, B. Dennis and A. A. King, Experimental support of the scaling rule for demographic stochasticity, Ecological Letters 9 (2006), 537-547
- J. M. Cushing, Nonlinear semelparous Leslie models, Mathematical Biosciences and Engineering 3, No. 1 (2006), 17-36 (with ERRATA)
- J. M. Cushing and S. LeVarge, Some discrete competition models and the principle of competitive exclusion, Difference Equations and Discrete Dynamical Systems, Proceedings of the Ninth International Conference, (L. J. S. Allen, B. Aulbach, S. Elaydi, R. Sacker, editors), World Scientific, 2005 (ISBN 981-256-520-5), pp. 283-302
- R.
F. Costantino, R. A. Desharnais, J.
M. Cushing, B. Dennis, S. M. Henson and A. A. King, The
flour beetle
*Tribolium*as an effective tool of discovery, Advances in Ecological Research, Volume 37 (2005), 101-141 - S. R.-J. Jang and J. M. Cushing, Dynamics of hierarchical models in discrete-time, Journal of Difference Equations and Applications 11, No. 2 (2005), 95-116
- J. M. Cushing, S. Levarge, N. Chitnis, S. M. Henson, Some discrete competition models and the competitive exclusion principle, Journal of Difference Equations and Applications 10, No. 13-15 (2004), 1139-1151
- J. M. Cushing, The LPA model, Fields Institute Communications 43 (2004), 29-55
- J. M. Cushing, Population dynamics, in The Encyclopedia of Nonlinear Science, (A. Scott, editor) Routledge, Taylor and Francis Group, New York, 2004
- A.
A. King, R. F. Costantino, J. M.
Cushing, S. M. Henson, R. A. Desharnais and B. Dennis, Anatomy
of a chaotic attractor: subtle model predicted patterns revealed in
population data, Proceedings
of
the National Academy of Sciences 101,
No. 1 (2003), 408-413

- S. M. Henson, A. A. King, R. F. Costantino, J. M. Cushing, B. Dennis, R. A. Desharnais, Explaining and predicting patterns in stochastic population systems, Proceedings of the Royal Society, London B 270 (2003), 1549-1553
- S. M. Henson, J. R. Reilly, S. L. Robertson, M. C. Schu, E. W. Davis and J. M. Cushing, Predicting irregularities in population cycles, SIAM Journal on Applied Dynamical Systems 2, No. 2 (2003), 238-253
- J. Edmunds, J. M. Cushing, R. F. Costantino, S. M. Henson, B. Dennis and R. A. Desharnais, Park's Tribolium competition experiments: a non-equilibrium species coexistence hypothesis, Journal of Animal Ecology 72 (2003), 703-712
- B. Dennis, R. A. Desharnais, J. M. Cushing, S. M. Henson and R. F. Costantino, Can noise induce chaos?, Oikos 102 (2003), 329-340
- J. M. Cushing, Cycle chains and the LPA model, Journal of Difference Equations and Applications 9, No. 7 (2003), 655-670
- S. R.-J. Jang and J. M. Cushing, A discrete hierarchical model of intra-specific competition, Journal of Mathematical Analysis and Applications 280 (2003), 102-122
- J. M. Cushing, S. M. Henson, A periodically forced Beverton-Holt equation, Journal of Difference Equations and Applications 8, No. 12 (2002), 1119-1120
- A.
A. King, R. A. Desharnais, S. M.
Henson, R. F. Costantino, J. M. Cushing and B. Dennis, Letter to
editor: Random
perturbations and
lattice effects in chaotic population dynamics
, Science 297
(27 September,
2002),
2163

- S. M. Henson, R. F. Costantino, J. M. Cushing, B. Dennis and R. A. Desharnais, Basins of attraction: population dynamics with two locally stable 4-cycles, Oikos 98 (2002), 17-24
- S. M. Henson, J. M. Cushing, Geometric transient solutions of autonomous scalar maps, Journal of Difference Equations and Applications 8 (2002), 61-73
- J. M. Cushing and S. M. Henson, Global dynamics of some periodically forced, monotone difference equations, Journal of Difference Equations and Applications 7 (2001), 859-872
- S. M. Henson, R. F. Costantino, J. M. Cushing, R. A. Desharnais, B. Dennis and A. A. King, Lattice effects observed in chaotic dynamics of experimental populations, Science 294 (19 Oct 2001), 602-605
- R. A. Desharnais, R. F. Costantino, J. M. Cushing, S. M. Henson and B. Dennis, Chaos and population control of insect outbreaks, Ecology Letters 4, No. 3 (2001), 229-235
- B. Dennis, R. A. Desharnais, J. M. Cushing, S. M. Henson and R. F. Costantino, Estimating chaos and complex dynamics in an insect population, Ecological Monographs 71, No. 2 (2001), 277-303
- J. M. Cushing, S. M. Henson, B. Dennis and R. A. Desharnais, R. F. Costantino and A. King, A chaotic attractor in ecology: theory and experimental data, Chaos, Solitons & Fractals 12, (2001), 219-234
- S. M. Henson, R. F. Costantino, J. M. Cushing, B. Dennis and R. A. Desharnais, Multiple attractors, saddles and population dynamics in periodic habitats, Bulletin of Mathematical Biology 61 (1999), 1121-1149
- J. M. Cushing, Global stability of some matrix equations in population dynamics, Journal of Difference Equations and Applications 5, No. 6 (1999), 557-560
- S. M. Henson, J. M. Cushing, R. F. Costantino, B. Dennis and R. A. Desharnais, Phase Switching in biological population, Proceedings of the Royal Society 265 (22 November 1998), 2229-2234
- Zhou Yicang and J.M. Cushing, Stability conditions for equilibria of nonlinear matrix population models, Journal of Difference Equations & Applications 4 (1998), 95-126
- J. M. Cushing, R. F. Costantino, B. Dennis, R. A. Desharnais and S. M. Henson, Nonlinear population dynamics: models, experiments, and data, Journal of Theoretical Biology 194, No. 1 (1998), 1-9
- J. M. Cushing, Periodically forced nonlinear systems of difference equations, Journal of Difference Equations and Applications 3 (1998), 547-561
- R. F. Costantino, J. M. Cushing, B. Dennis, R. A. Desharnais and S. M. Henson, Resonant population cycles in temporally fluctuating habitats, Bulletin of Mathematical Biology 60, No. 2 (1998), 247-275
- S. M. Henson and J. M. Cushing, The effect of periodic habitat fluctuations on a nonlinear insect population model, Journal of Mathemathical Biology 36 (1997), 201-226
- J. M. Cushing, B. Dennis, R. A. Desharnais and R. F. Costantino, Moving toward an unstable equilibrium: saddle nodes in population systems, Journal of Animal Ecology 67, No. 1 (1998), 298-306
- B. Dennis, R. A. Desharnais, J. M. Cushing and R. F. Costantino, Transitions in population dynamics: equilibria to periodic cycles to aperiodic cycles, Journal of Animal Ecology 66 (1997), 704-729
- R. F. Costantino, R. A. Desharnais, J. M. Cushing and B. Dennis, Letter to the editor: Estimating chaos in an insect population, Science 276 (June 1997), 1881-1882
- J.
M. Cushing, Nonlinear matrix
equations and population dynamics, Chapter 6 in
*Structured Population Models in Marine, Terrestrial, and Freshwater Systems*(Shripad Tuljapurkar and Hal Caswell, eds.), Population and Community Biology Series 18, Chapman and Hall, New York, 1997 - R.
F. Costantino, R. A. Desharnais, J.
M. Cushing and B. Dennis, Chaotic
dynamics
in an insect population, Science
275 (January 1997), 389-391

- J. M. Cushing, B. Dennis, R. A. Desharnais and R. F. Costantino, An interdisciplinary approach to understanding nonlinear ecological dynamics, Ecological Modelling 92 (1996), 111-119
- S. M. Henson and J. M. Cushing, Hierarchical models of intra-specific competition: scramble versus contest, Journal of Mathematical Biology (1996) 34, 755-772
- S. M. Henson and J. M. Cushing, Optimal parasitization in a size-structured host-parasitoid model, Nonlinear World 3 (1996), 1-18
- J. M. Cushing, Periodic cycles of nonlinear discrete renewal equations, Journal of Difference Equations & Applications 2 (1996), 117-137
- J. M. Cushing, Competition in hierarchically size-structured populations, Differential Equations and Applications to Biology and to Industry (Martelli, Cooke, Cumberbatch, Tang and Thieme, editors), World Scientific, Singapore, 1996 pp: 71-80
- Yang Kuang and J. M. Cushing, Global stability in a nonlinear difference-delay equation model of flour beetle population growth, Journal of Difference Equations and Applications 2 (1995), pp. 31-37
- J. M. Cushing, Systems of difference equations and structured population dynamics, Proceedings of the First International Conference on Difference Equations (Saber N. Elaydi, John R. Graef, Gerry Ladas, Allan C. Peterson, editors), Gordon and Breach Publishers, US, 1995, pp. 123-132
- B. Dennis, R. A. Desharnais, J. M. Cushing and R. F. Costantino, Nonlinear demographic dynamics: mathematical, models, statistical methods, and biological experiments, Ecological Monographs 65 (3), 1995, 261-281
- R.
F. Costantino, J. M. Cushing, B.
Dennis and R. A. Desharnais, Experimentally
induced transitions in the dynamics behaviour of insect populations,
Nature
375 (1995, May),
227-230

- J. M. Cushing and Jia Li, Oscillations caused by cannibalism in a size-structured population model, Canadian Applied Mathematics Quarterly 3 (1995), No. 2. 155-172
- J. M. Cushing, Nonlinear Matrix Models for Structured Population, Chapter 26 in Mathematical Population Dynamics III: Mathematical Methods and Modelling of Data, O. Arino, D. Axelrod, M. Kimmel, & M. Langlais, eds.,Wuerz Publishing Ltd, 1995
- J. M. Cushing, Structured Population Dynamics, Frontiers in Mathematical Biology, Lecture Notes in Biomathematics, Vol. 100, edited by S. A. Levin, Springer, Berlin, 1995, 280-295
- J. M. Cushing and Zhou Yicang, The net reproductive value and stability in structured population models, Natural Resource Modeling 8, No. 4 (1994), 1-37
- J. M. Cushing, Oscillations in age-structured population models with an Allee effect, Journal of Computational and Applied Mathematics 52, 1994, 71-80
- K. M. Crowe and J. M. Cushing, Optimal instar parasitization in a stage structured host-parasitoid model, Natural Resource Modeling 8, No. 2, 1994, 119-138
- J. M. Cushing, The dynamics of hierarchical age-structured populations, Journal of Mathematical Biology 32 (1994), 705-729
- J. M. Cushing, A size-structured model for cannibalism, Theoretical Population Biology 42 (1992), 347-361
- J. M. Cushing and Jia Li, Intra-specific competition and density dependent juvenile growth, Bulletin of Mathematical Biology 53, No. 4 (1992), 503-519
- J. M. Cushing, A discrete model of competing size-structured species, Theoretical Population Biology 41, No. 2 (1992), 372-387
- J. M. Cushing and Jia Li, The dynamics of a size-structured intraspecific competition model with density dependent juvenile growth rates, Chapter 6 in Individual Based Modeling: Concepts and Models, (D. DeAngelis and L.J. Gross, eds.), Routledge, Chapman and Hall, New York, 1992, 112-125
- J. M. Cushing, David Gay, Larry Grove, David Lomen and David Lovelock, The Arizona experience: software development & use, Proceedings of the Third International Conference on Techonology in Collegiate Mathematics, Addison-Wesley Publishing Company, 1992, 41-47
- J.
M. Cushing, Some delay models for
juvenile vs. adult competition,
*Differential Equations & Applications in Biology and Population Dynamics*(Busenberg & Martelli, editors), Springer, 1991, 177-188 - J. M. Cushing, A simple model of cannibalism, Mathematical Biosciences 107, No.1, (1991), 47-72
- J. M. Cushing and Jia Li, Juvenile versus adult competition, Journal of Mathematical Biology 29 (1991), 457-473
- J. M. Cushing, Competing size-structured species, Mathematical Population Dynamics (Chapter 3, p. 27-44), O. Arino, D.E. Axelrod and M. Kimmel eds., Marcel Dekker, Inc., NY 1991
- J. M. Cushing, Some competition models for size-structured populations, Rocky Mountain Journal of Mathematics 20, No. 4 (1990), 879-897
- J. M. Cushing, A strong ergodic theorem for some nonlinear matrix models for structured population growth, Natural Resource Modeling 3, No. 3 (1989), 331-357
- J. M. Cushing and Jia Li, On Ebenman's model for the dynamics of a population with competing juveniles and adults, Bulletin of Mathematical Biology 51, No. 6, (1989), 687-713
- J. M. Cushing, A competition model for size-structured species, SIAM Journal of Applied Mathematics 49, No. 3 (1989), 838-858
- J.
M. Cushing, The Allee effect in
age-structured population dynamics,
*Mathematical Ecology*(S.A. Levin & T. Hallam, editors), World Scientific, New Jersey, 1988, 479-505 - J. M. Cushing, Nonlinear matrix models and population dynamics, Natural Resource Modeling 2, No. 4 (1988), 539-580
- J. M. Cushing, Equilibria and oscillations in age-structured population growth models, Mathematical Modelling of Environmental and Ecological Systems (edited by J. B. Shukla, T.G. Hallam, & V. Capasso), Elsevier Science Publishers, NY, 1987, 153-175
- J. M. Cushing, Equilibria in systems of interacting structured populations, Journal of Mathematical Biology 24 (1987), 627-649
- J. M. Cushing, Oscillatory population growth in periodic environments, Theoretical Population Biology 30, no 3 (1986), 289-308
- J.
M. Cushing,
Periodic
McKendrick equations for age-structured population growth,
*Computers and Mathematics with Applications*12A, No. 45 (1986), 513-526 (Reprinted in*Advances in Hyperbolic Differential Equations Vol. 3*, edited by M. Witten, Pergamon Press, 1986) - J. M. Cushing, Periodic Lotka-Volterra competition equations, Journal of Mathematical Biology 24 (1986), 381-403
- J. M. Cushing, Equilibria in structured populations, Journal of Mathematical Biology 23, No. 1 (1985), 15-39
- J.
M. Cushing, Global
branches of
equilibrium solutions of the McKendrick equations for age-structured
population growth, Computers
and
mathematics with Applications 11
(1985), 175-188 (Reprinted in
*Advances in Hyperbolic Differential Equations Vol. 2*, edited by M. Witten, Pergamon Press, 1985) - J.
M. Cushing, Equilibrium solutions of
general age-structured population growth equations, Mathematical Models of
Renewable Resources
3 (1985), 104-108

- J. M. Cushing, Periodic McKendrick equations, Proceedings of the IMACS World Congress, Olso, Norway, 1985
- J. M. Cushing, Existence and stability of equilibria in age-structured population dynamics, Journal of Mathematical Biology 20, No. 3 (1984), 259-276
- J. M. Cushing, Periodic two-predator, one-prey interactions and the time sharing of a resource niche, SIAM Journal of Applied Mathematics 44, No. 2 (1984), 392-410
- J. M. Cushing and M. Saleem, A competition model with age-structure, Lecture Notes in Biomathematics 54, Springer, New York, 1984,178-192
- J. M. Cushing, Bifurcation of time periodic solutions of the McKendrick equations with applications to population dynamics, Computers and Mathematics with Applications 9, No. 3 (1983), 459-478 (Reprinted in Advances in Hyperbolic Differential Equations, Volume 1, edited by M. Witten, Pergamon Press, 1983)
- J. M. Cushing, Periodic Lotka-Volterra systems and time sharing of ecological niches, Lecture Notes in Biomathematics 52, pp 342-348, Springer, New York, 1983
- J. M. Cushing and M. Saleem, A predator-prey model with age structure, Journal of Mathematical Biology 14 (1982), 231-250
- J. M. Cushing, Periodic Kolmogorov systems, SIAM Journal of Mathematical Analysis 13, No. 5 (1982), 811-827
- J.
M. Cushing, Bifurcation of periodic
solutions of nonlinear equations in age-structured population dynamics,
Nonlinear
Phenomena in
Mathematical Sciences (V.
Lakshmikantham, Ed.), 279-288 Academic
Press, 1982, 279-288

- J. M. Cushing, Stability and maturation periods in age-structured populations, Differential Equations and Applications in Ecology, Epidemics and Population Dynamics (Busenberg and Cooke, editors), 163-182, Academic Press, NY, 1981
- J. M. Cushing and S. D. Simmes, Bifurcation of asymptotically periodic solutions of Volterra integral equations, Journal of Integral Equations 4 (1980), 339-361
- J. M. Cushing, Model stability and instability in age structured populations, Journal of Theoretical Biology 86 (1980), 709-730
- J. M. Cushing, Two species competition in a periodic environment, Journal of Mathematical Biology 10 (1980), 385-400
- J. M. Cushing, Stability and instability in predator-prey models with growth rate response delays, Rocky Mountain Journal of Mathematics 9, No. 1 (1979), 43-50
- J. M. Cushing, Nontrivial periodic solutions of integrodifferential equations, Journal of Integral Equations 1, No. 2 (1979), 165-181
- J.
M. Cushing, Nontrivial
periodic
solutions
of
some
Volterra integral equations, Lecture
Notes in Mathematics, Vol.
737, Springer, New York, 1979, 50-66,
DOI:10.1007/BFb0064495

- J.
M. Cushing, Volterra Integrodifferential Equations in Population
Dynamics, Mathematics
of Biology (M. Iannelli, editor), Proc. 1979 C.I.M.E.
Summer School, Florence, Italy, ISBN 978-3-642-11069-6,
Springer-Verlag, Berline Heidelberg 2010

- J. M. Cushing, Bifurcation of periodic oscillations due to delays in single species growth models, Journal of Mathematical Biology 6 (1978), 145-161
- J. M. Cushing, Strongly admissible operators and Banach space solutions of nonlinear equations, Funkcialaj Ekvacioj 20, No. 3 (1977), 237-245
- J. M. Cushing, On the oscillatory nature of general predator-prey models with delays, Journal of Nonlinear Analysis 1, No. 6 (1977), 583-592
- J. M. Cushing, Bifurcation of periodic solutions of integro-differential equations with applications to time delay models in population dynamics, SIAM Journal of Applied Mathematics 33, No. 4 (1977), 640-654
- J. M. Cushing, Stable positive periodic solutions of the time dependent logistic equation under possible hereditary influences, Journal of Mathematical Analysis and Applications 3 (1977), 747-754
- J. M. Cushing, Time delays in single species growth models, Journal of Mathematical Biology 3 (1977), 257-264
- J. M. Cushing, Periodic time-dependent predator-prey systems, SIAM Journal of Applied Mathematics 32, No. 1 (1977), 82-95
- J. M. Cushing, Time delays in predator-prey systems, Nonlinear Systems and Applications (V. Lakshmikantham, ed.), 469-472, Academic Press, New York, 1977
- J. M. Cushing, Admissible operators and solutions of perturbed operator equations, Funkcialaj Ekvacioj 19 (1976), 79-84
- J. M. Cushing, Bounded solutions of perturbed Volterra integro-differential systems, Journal of Differential Equations 20, No.1 (1976), 61-70
- J. M. Bownds, J. M. Cushing and R. Schutte, Existence, uniqueness and extendability of solutions of Volterra integral equations with multiple, variable lags, Funkcialaj Ekvacioj 19 (1976), 101-111
- J. M. Cushing, Extremal tests for functions of several real variables at degenerate critical points, Aequationes Mathematicae 13 (1976), 89-96
- J. M. Cushing, Forced asymptotically periodic solutions of predator-prey systems with or without hereditary effects, SIAM Journal of Applied Mathematics 30, No. 4 (1976), 665-674
- J. M. Cushing, Periodic solutions of two species interaction models with lags, Mathematical Biosciences 31 (1976), 143-156
- J. M. Cushing, Periodic solutions of Volterra's population equation with hereditary effects, SIAM Journal of Applied Mathematics 31, No. 2 (1976), 251-260 (Erratum, SIAM Journal of Applied Mathematics 32, No. 2 (1977), 895)
- J. M. Cushing, Predator-prey interactions with time delays, Journal of Mathematical Biology 3 (1976), 369-380
- J. M. Cushing, Stable limit cycles of time dependent multi-species interactions, Mathematical Biosciences 31 (1976), 259-273
- J. M. Bownds and J. M. Cushing, On preserving stability of Volterra integral equations under a general class of perturbations, Mathematical Systems Theory 9, No. 2 (1975), 117-131
- J. M. Bownds and J. M. Cushing, On the behavior of solutions of predator-prey equations with hereditary terms, Mathematical Biosciences 26 (1975), 41-54
- J. M. Cushing, An operator equation and bounded solutions of integro-differential systems, SIAM Journal of Mathematical Analysis 6, No. 3 (1975), 433-445
- J. M. Bownds and J. M. Cushing, Some stability theorems for systems of Volterra integral equations, Applicable Analysis 5 (1975), 65-78
- J. M. Cushing, Stability of perturbed Volterra integral equations, Journal of Mathematical Analysis and Applications 50, No. 2 (1975), 325-340
- J. M. Cushing, Nonlinear Steklov problems on nonsymmetric domains, Journal of Mathematical Analysis and Applications 43 (1973), 743-753
- J. M. Bownds and J. M. Cushing, On strong stability for linear integral equations, Mathematical Systems Theory 7, No. 3 (l973), 193-200
- J. M. Bownds and J. M. Cushing, A representation formula for linear Volterra integral equations, Bulletin of the American Mathematics Society 79, No. 3 (1973), 532-536
- J. M. Bownds and J. M. Cushing, Strong stability of perturbed systems of Volterra integral equations, Mathematical Systems Theory 7, No. 4 (1973), 360-366
- J. M. Cushing, Nonlinear Steklov problems on the unit circle II (and a hydrodynamical applications), Journal of Mathematical Analysis and Applications 39, No. 2 (1972), 267-278
- J. M. Cushing, Nonlinear Steklov problems on the unit circle I, Journal of Mathematical Analysis and Applications 38, No. 3 (1972), 766-783
- J. M. Bownds and J. M. Cushing, Some stability criteria for linear systems of Volterra integral equations, Funkcialaj Ekvacioj 15, No. 2 (1972), 101-117
- J. M. Cushing, Some existence results for Nonlinear Steklov problems, Lecture Notes in Mathematics, Vol. 280, 236-240, Springer, New York, 1972
- J. M. Cushing, Global branches of solutions to nonlinear elliptic eigenvalue problems, Indiana University Mathematics Journal 20, No. 11 (1971), 1035-1045
- J. M. Cushing, Some existence theorems for nonlinear eigenvalue problems associated with elliptic equations, Archive of Rational Mechanics and Analysis 42, No. 1 (1971), 63-76
- J. M. Cushing, A uniqueness criterion for harmonic functions under nonlinear boundary conditions, Journal of Mathematical Analysis and Applications 33, No. 2 (1971), 443-448
- J. M. Cushing, Uniqueness of positive solutions to nonlinear elliptic equations, SIAM Journal of Mathematical Analysis 2, No. 2 (1971), 290-292
- J. M. Cushing and D. R. Dunninger, Uniqueness theorems under nonlinear boundary conditions for some quasi-linear elliptic equations, Journal of Mathematical Analysis and Applications 33, No. 3 (l971), 114-127
- J. M. Cushing, Local uniqueness for harmonic functions under nonlinear boundary conditions, Journal of Differential Equations 8, No. 3 (1970), 512-522
- J. M. Cushing, On a conjecture of Levi-Civita, Journal of Mathematics and Mechanics 19, No. 12, (1970), 1047-1050
- J. M. Cushing, Uniqueness and comparison of harmonic functions under nonlinear boundary conditions, Journal of Mathematical Analysis and Applications 28, No. 3 (1969), 581-589

J. M. Cushing / Department of Mathematics / Program in Applied Mathematics / University of Arizona / Tucson, AZ 85721-0089

(revised 29 February 2024)

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