Undergraduate Research Project

Department of Mathematics
University of Arizona

Synchronization of chaos, delay, and application to the Ikeda map

The faculty involved in this project were Nick Ercolani, Robert Indik and Joceline Lega.

The participants were three junior Mathematics majors and one junior Physics major. It was possible to financially support all of the student participants. The research activities took place in the Arizona Center for Mathematical Sciences (ACMS) where conference rooms and computational facilities for the project are available.

Students' Reports

Project Organization

The organization of this project was based on a weekly 2 hour working session and an open ended weekly computer lab session. Funding was available to support all of the student participants. Each student was assigned to one of the faculty participants who served as the student's mentor. This was the person whom the student consulted regularly and who assessed his progress.

Most of the students involved in this project had worked on the 1997-1998 project with the same faculty members and all of them had taken a 400-level course on dynamical systems with Nick Ercolani in the Fall of 1998. The project, which only ran in the Spring of 1999, thus started at a faster pace. Initially, the faculty introduced the laser models and basic ideas on the dynamical systems approach to maps. The rest of the weekly sessions was devoted to discussion of the students' results.

Students really became quite independent in proposing ideas and conjectures to faculty and seeking out new tools. The projects reports listed above were written by the students in LaTex and reflect their own understanding of the proposed research and their own analysis of the results they obtained.

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