Distinct collective states due to the trade-off between attractive and repulsive couplings

TL;DR

This paper explores how attractive and repulsive couplings in oscillator networks create complex collective states, including cluster chimera death, with transitions influenced by a control parameter and coupling range.

Contribution

It introduces a control parameter in repulsive coupling that reveals new collective patterns and transition routes in nonlocally coupled oscillators.

Findings

Emergence of cluster chimera death states

Oscillatory cluster states with distinct dynamical groups

Power law decay of coherent domain number with coupling range

Abstract

We investigate the effect of repulsive coupling together with an attractive coupling in a network of nonlocally coupled oscillators. To understand the complex interaction between these two couplings we introduce a control parameter in the repulsive coupling which plays a crucial role in inducing distinct complex collective patterns. In particular, we show the emergence of various cluster chimera death states through a dynamically distinct transition route, namely the oscillatory cluster state and coherent oscillation death state as a function of the repulsive coupling in the presence of the attractive coupling. In the oscillatory cluster state, the oscillators in the network are grouped into two distinct dynamical states of homogeneous and inhomogeneous oscillatory states. Further, the network of coupled oscillators follows the same transition route in the entire coupling range. Depending upon distinct coupling ranges the system displays a different number of clusters in the death state and oscillatory state. We also observe that the number of coherent domains in the oscillatory cluster state exponentially decreases with increase in coupling range and obeys a power law decay. Additionally, we show analytical stability for observed solitary state, synchronized state, and incoherent oscillation death state.