Shear induced symmetry breaking dynamical states

TL;DR

This paper investigates how shear influences the emergence of various symmetry-breaking dynamical states in a coupled oscillator system, revealing new patterns and validating stability conditions through analytical and numerical methods.

Contribution

It introduces the impact of shear on symmetry-breaking states in coupled oscillators, identifying new dynamical patterns and providing analytical stability validation.

Findings

Shear induces diverse dynamical patterns including amplitude clusters and solitary states.

Analytical stability conditions for oscillation death are validated against numerical results.

Shear leads to the emergence of inhomogeneous oscillation death and oscillatory cluster states.

Abstract

We examine how shear influences the emergence of symmetry-breaking dynamical states in a globally coupled Stuart-Landau (SL) oscillator system with combined attractive and repulsive interactions. In the absence of the shear parameter, the system exhibits synchronization, nontrivial oscillation death states, and oscillation death states. However, with the introduction of the shear parameter, we observe diverse dynamical patterns, including amplitude clusters, solitary states, complete synchronization, and nontrivial oscillation death states when the repulsive interaction is weak. As the strength of the repulsive interaction increases, the system becomes more heterogeneous, resulting in imperfect solitary states. We also validate the analytical stability condition for the oscillation death region and compare it with the numerical boundary, finding a close match. Furthermore, we discover that the presence of shear leads to the emergence of symmetry-breaking dynamical states, specifically inhomogeneous oscillation death states and oscillatory cluster states under nonlocal coupling interaction.