# Transition to Turbulence in Driven Active Matter

## TL;DR

This paper investigates a Lorenz-like model for driven active matter, revealing a transition to chaos via period-doubling bifurcations and identifying a unique route to turbulence in such systems.

## Contribution

It introduces the first Lorenz-like model demonstrating a sequence of period-doubling bifurcations leading to turbulence in active matter.

## Key findings

- Passage to chaos through period-doubling bifurcations.
- Coexistence of strange attractor and fixed points beyond homoclinic point.
- Disappearance of strange attractor at Hopf point, leading to limit cycle.

## Abstract

A Lorenz-like model was set up recently, to study the hydrodynamic instabilities in a driven active matter system. This Lorenz model differs from the standard one in that all three equations contain non-linear terms. The additional non-linear term comes from the active matter contribution to the stress tensor. In this work, we investigate the non-linear properties of this Lorenz model both analytically and numerically. The significant feature of the model is the passage to chaos through a complete set of period-doubling bifurcations above the Hopf point for inverse Schmidt numbers above a critical value. Interestingly enough, at these Schmidt numbers a strange attractor and stable fixed points coexist beyond the homoclinic point. At the Hopf point, the strange attractor disappears leaving a high-period periodic orbit. This periodic state becomes the expected limit cycle through a set of bifurcations and then undergoes a sequence of period-doubling bifurcations leading to the formation of a strange attractor. This is the first situation where a Lorenz-like model has shown a set of consecutive period-doubling bifurcations in a physically relevant transition to turbulence.