Transition to turbulence in driven active matter

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 nonlinear terms. The additional nonlinear term comes from the active matter contribution to the stress tensor. In this work, we investigate the nonlinear 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 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.