Emerging chimera states under non-identical counter-rotating oscillators

TL;DR

This paper investigates the emergence and robustness of chimera states in non-identical counter-rotating oscillators, revealing partial symmetry breaking and transitions between various synchronized states influenced by perturbations.

Contribution

It introduces the concept of partial P-symmetry breaking in chimera states and demonstrates their occurrence in non-identical counter-rotating oscillator networks with perturbations.

Findings

Chimera states exhibit partial P-symmetry preservation.

Transition from incoherent to coherent mixed synchronization occurs via chimera states.

Chimera states are robust in larger networks and across different oscillator models.

Abstract

Frequency plays a crucial role in exhibiting various collective dynamics in the coexisting co- and counter-rotating (CR) systems. To illustrate the impact of CR frequencies, we consider a network of non-identical and globally coupled Stuart-Landau oscillators with additional perturbation. Primarily, we investigate the dynamical transitions in the absence of perturbation, demonstrating that the transition from desynchronized state to cluster oscillatory state occurs through an interesting partial synchronization state. Followed by this, the system dynamics transits to amplitude death and oscillation death states. Importantly, we find that the observed dynamical states do not preserve the parity(P) symmetry in the absence of perturbation. When the perturbation is increased one can note that the system dynamics exhibits a new kind of transition which corresponds to a change from incoherent mixed synchronization to coherent mixed synchronization through chimera state. In particular, incoherent mixed synchronization and coherent mixed synchronization states completely preserve the P-symmetry, whereas the chimera state preserves the P-symmetry only partially. To demonstrate the occurrence of such partial symmetry breaking (chimera) state, we use basin stability analysis and discover that PSB exists as a result of the coexistence of symmetry preserving and symmetry breaking behavior in the initial state space. Further, a measure of the strength of P-symmetry is established to quantify the P-symmetry in the observed dynamical states. Finally, by increasing the network size, the robustness of the chimera is also inspected and we find that the chimera state is robust even in networks of larger sizes. We also show the generality of the above results in the related phase reduced model as well as in other coupled models such as the globally coupled van der Pol and R\"ossler oscillators.