9/13/2023
Chaos and homeostasis
in multiple timescales dynamics
in multiple timescales dynamics
Jonathan Touboul
Department of Mathematics
Brandeis University
Complex nonlinear and network dynamics, as observed in many biological systems, are prone to generate irregular chaotic activity. Fortunately, in nature, these systems are still able to maintain essential biological function, and may be robust to changes in the environment despite the chaotic nature of their behavior. This however may break down into irregular erratic activity upon changes in the environment. I will present a theory of how chaotic systems with multiple timescales may maintain regular macroscopic dynamics and how these subsequently break down. We focus our examples on chaotic models of neural activity, where experiments report such transitions in qualitative behavior, but the mechanisms we describe are universal for systems featuring relaxation cycles through chaotic attractors.