Complex nonlinear and network dynamics, as observed in many biological systems, are prone to generate complex 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 their chaotic nature, until they break down and generate irregular erratic activity. 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.

This a joint work with Evelyn Sander and Jonathan Jaquette.