Different kinds of chimera death states in nonlocally coupled oscillators

TL;DR

This paper explores how the nonisochronicity parameter influences the formation and structure of chimera death states in nonlocally coupled Stuart-Landau oscillators, revealing new types and scaling laws.

Contribution

It introduces the concept of different chimera death states induced by nonisochronicity and analyzes their structural properties and robustness in a nonlocal oscillator network.

Findings

Different types of chimera death states are identified.

The number of periodic domains decreases exponentially with coupling range.

Chimera death states are robust to frequency perturbations.

Abstract

We investigate the significance of nonisochronicity parameter in a network of nonlocally coupled Stuart-Landau oscillators with symmetry breaking form. We observe that the presence of nonisochronicity parameter leads to structural changes in the chimera death region while varying the strength of the interaction. This gives rise to the existence of different types of chimera death states such as multi-chimera death state, type-I periodic chimera death (PCD) state and, type-II periodic chimera death (PCD) state. We also find that the number of periodic domains in both the types of PCD states exponentially decreases with an increase of coupling range and obeys a power law under nonlocal coupling. Additionally, we also analyze the structural changes of chimera death states by reducing the system of dynamical equations to a phase model through the phase approximation. We also briefly study the role of nonisochronicity parameter on chimera states, where the existence of multi-chimera state with respect to the coupling range is pointed out. Moreover, we also analyze the robustness of the chimera death state to perturbations in the natural frequencies of the oscillators.