Dynamic Instabilities and Pattern Formation in Chemotactic Active Matter

TL;DR

This paper investigates how collective chemotaxis influences motility-induced phase separation in active matter, revealing conditions under which chemotaxis suppresses or induces new dynamic patterns, supported by analytical and simulation results.

Contribution

It provides a comprehensive analysis of the interplay between chemotaxis and phase separation, introducing new stability criteria and pattern formation mechanisms in active matter systems.

Findings

Chemotaxis can suppress or arrest MIPS.

Identification of four bifurcation types leading to pattern formation.

Analytical expressions match simulation results quantitatively.

Abstract

Collectives of actively-moving particles can spontaneously segregate into dilute and dense phases through a process known as motility-induced phase separation (MIPS). This captivating phenomenon is well-studied for randomly-moving particles with no directional bias. However, many active systems perform collective chemotaxis -- directed motion along a chemical gradient collectively generated by the particles themselves through consumption or production. Here, we use linear stability analysis, amplitude equations, and numerical simulations to study how MIPS is influenced by collective chemotaxis. We find that chemotaxis can either arrest or entirely suppress MIPS, or give rise to novel dynamic instabilities such as traveling waves and spirals. We predict the stability region of the stationary and oscillatory patterns and identify four types of bifurcation that can arise: pitchfork, saddle-node, infinite period, and supercritical Hopf. We also derive analytical expressions for the amplitude of the pattern and traveling wave velocity, yielding excellent quantitative agreement with simulations. Furthermore, we generalize our model to study particles that either consume or produce chemoattractant or chemorepellent, as well as mixtures of particles with different chemotactic behaviors. By establishing quantitative principles describing the competition between MIPS and chemotaxis, our study helps deepen understanding of the rich physics underlying chemically-responsive active matter systems.