Oct 28, 2022
Contact: Sarah Day
Summary
{{https://gmumathmaker.notion.site/gmumathmaker/Evelyn-Sander-fea8974a425643178781cf995db94f58, Evelyn Sander}} (George Mason University)
Full Description
Title: Reliability and robustness of oscillations in some slow-fast chaotic systems
Abstract:
Nonlinear systems in interaction, often used to describe biological systems, are prone to generate complex chaotic activity. Yet, many experimental observations reported robustness of biological systems to changes in external or internal conditions. I will speak about a refinement of the notion of chaos that reconciles chaos and biological robustness in chaotic systems with multiple timescales. In this case, systems displaying relaxation cycles going through strange attractors do generate chaotic dynamics that are regular at macroscopic timescales, thus consistent with physiological function. However, this relative regularity breaks down through a universal global bifurcation, beyond which the system generates erratic activity also at slow timescales. This approach focuses on the fine analysis of an example system describing nerve cell activity and data in a crustacean central pattern generator. Beyond this example, we show that the passage of slow relaxation cycles through a strange attractor crises is a universal mechanism for the transition in such dynamics.
This is joint work with Jonathan Jaquette, Sonal Kedia, and Jonathan D. Touboul
