Stationary broken parity states in active matter models

TL;DR

This paper shows that many active matter models exhibit nongeneric stationary asymmetric states due to broken gradient structure, and identifies how to modify models to recover generic behavior with drifting states.

Contribution

It reveals the nongeneric behavior of active matter models with broken gradient structure and proposes modifications to restore generic drifting asymmetric states.

Findings

Asymmetric stationary states exist without pinning in certain active models.

These states only drift after a bifurcation as activity increases.

Modifications can restore generic drifting states in the models.

Abstract

We demonstrate that several nonvariational continuum models commonly used to describe active matter as well as other active systems exhibit nongeneric behavior: each model supports asymmetric but stationary localized states even in the absence of pinning at heterogeneities. Moreover, such states only begin to drift following a drift-transcritical bifurcation as the activity increases. Asymmetric stationary states should only exist in variational systems, i.e., in models with gradient structure. In other words, such states are expected in passive systems, but not in active systems where the gradient structure of the model is broken by activity. We identify a "spurious" gradient dynamics structure of these models that is responsible for this nongeneric behavior, and determine the types of additional terms that render the models generic, i.e., with asymmetric states that appear via drift-pitchfork bifurcations and are generically moving. We provide detailed illustrations of our results using numerical continuation of resting and steadily drifting states in both generic and nongeneric cases.