A Dynamical Systems Approach to Nonlinear Waves and Coherent Structures
In this talk I will discuss my approach to pattern forming phenomena in nonlinear systems. This work outlines a dynamical systems perspective to understand the existence, stability, dynamics, and bifurcations of nonlinear waves and coherent structures to mathematical equations. Particular focus is paid to understanding how symmetry of an equation can influence the solutions of differential equations and how breaking that symmetry changes the expected behaviour. I focus on both spiral waves and localized structures in this talk and demonstrate how using lattice dynamical systems can help us to better understand them from a mathematical point-of-view. This work shows how using lattice dynamical systems can be used to solve old problems from a new angle.