Chaotic heteroclinic networks as models of switching behavior in biological systems

TL;DR

This paper introduces chaotic heteroclinic networks as a deterministic, flexible model for biological switching behavior, capable of reproducing experimental data on organismal activity without relying on stochastic noise.

Contribution

The authors propose a novel class of chaotic heteroclinic network models that simulate biological state transitions deterministically, with tunable parameters controlling transition statistics and behavior.

Findings

Successfully reconstructed experimental dwell times and transition statistics for C. elegans.

Demonstrated the model's ability to replicate biological switching behavior across various conditions.

Showed that the model can handle complex architectures without increasing phase dimension.

Abstract

Key features of biological activity can often be captured by transitions between a finite number of semi-stable states that correspond to behaviors or decisions. We present here a broad class of dynamical systems that are ideal for modeling such activity. The models we propose are chaotic heteroclinic networks with nontrivial intersections of stable and unstable manifolds. Due to the sensitive dependence on initial conditions, transitions between states are seemingly random. Dwell times, exit distributions, and other transition statistics can be built into the model through geometric design and can be controlled by tunable parameters. To test our model's ability to simulate realistic biological phenomena, we turned to one of the most studied organisms, {\it C. elegans}, well known for its limited behavioral states. We reconstructed experimental data from two laboratories, demonstrating the model's ability to quantitatively reproduce dwell times and transition statistics under a variety of conditions. Stochastic switching between dominant states in complex dynamical systems has been extensively studied and is often modeled as Markov chains. As an alternative, we propose here a new paradigm, namely chaotic heteroclinic networks generated by deterministic rules (without the necessity for noise). Chaotic heteroclinic networks can be used to model systems with arbitrary architecture and size without a commensurate increase in phase dimension. They are highly flexible and able to capture a wide range of transition characteristics that can be adjusted through control parameters.