Faculty Scholarly Dissemination Grants

Title

Periodicity and Chaos in Some Planar Discrete Dynamical Systems with Negative Feedback

Department

Mathematics Department

College

College of Liberal Arts and Sciences

Disciplines

Physical Sciences and Mathematics

Abstract

Oscillatory dynamics occur in many real-life applications such as, for example, circadian rhythms in gene regulatory networks. One way to better understand such oscillatory dynamics is to study mathematical models involving discrete dynamical systems with negative feedback interconnections. In this talk, I will discuss the oscillatory behavior of solutions to a class of discrete dynamical systems in the plane with negative feedback. More specifically, I will give some general yet simple criteria to determine when solutions of such discrete dynamical systems show oscillatory stability in the form of periodicity and when they exhibit oscillatory instability in the form of chaos.

Conference Name

2012 AMS (American Mathematical Society) Fall Eastern Sectional Meeting

Conference Location

Rochester Institute of Technology, Rochester, NY

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