# Mostly Biomathematics Lunchtime Seminar

#### Chaotic heteroclinic networks as models of switching behavior in biological systems

**Speaker:**
Megan Morrison, Postdoctoral Associate, NYU Courant

**Location:**
Warren Weaver Hall 1314

**Date:**
Tuesday, April 11, 2023, 12:45 p.m.

**Synopsis:**

Global activity in biological networks often transitions between many semi-stable states that correspond to dominant biological states, behaviors, or decisions. Transitions between these semi-stable states often appear to be random and are modeled with stochastic models such as Markov chains. We propose that chaotic heteroclinic networks can be used to model stochastic switching phenomena. The models we build are low-dimensional, deterministic dynamical systems. Transitions between states are seemingly stochastic and dwell times vary due to chaos in the system. Choices of eigenvalues at saddle fixed points and functions used to connect their stable and unstable manifolds give quantitative control of the transition dynamics. As a proof of concept, we build models that fit the dynamics and switching statistics of* C. elegans *neural activity and show that Markov Model dynamics, often used to model state switching in neural dynamics, can be reproduced with this framework. Stochastic switching in our model is generated by deterministic dynamics; using this model we show that neural activity may randomly roam between various states without the necessity for noise.