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

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 follow the same transition route in the entire coupling range. Depending upon distinct coupling ranges, the system displays 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.

Dynamics of multilayer networks with amplification

“…In the same vein, in the Refs. 42,43 the authors present some behaviour such as clusters, pattern formation, synchronization and so on according to the attractive and repulsive coupling.…”

Imperfect Amplitude Mediated Chimera States in a Nonlocally Coupled Network

“…In this report, we unravel the emergence distinct collective dynamical behavior in a network of nonlocally coupled Stuart-Landau oscillators with competing attractive and repulsive couplings. The trade-off between the attractive and repulsive couplings in many natural systems has been revealed as an essential element in determining their functional and evolutionary processes [39,40]. We find that the competing interaction between them facilitates the emergence of imperfect amplitude mediated chimera, which is characterized by a continuous drift of the oscillators between the homogeneous and the inhomogeneous oscillations as a function of time.…”

“…Domains of inhomogeneous death states are termed as cluster oscillation death states whereas coexisting domains of coherent and incoherent death states (of the inhomogeneous death states) constitute the cluster chimera death state. The number of clusters in the death states are found to vary as a function of the coupling range and cluster initial conditions in nonlocally coupled networks [4,39].…”

Amplitude mediated spiral chimera pattern in a nonlinear reaction-diffusion system

“…In contrast to classical chimera states, where the coherence-incoherence behaviors emerge depending on the phases of the constituents, in amplitude mediated chimera states [65,66] both the amplitudes and the phases of the oscillators exhibit random distribution in the incoherent domain. Interestingly, the appearance of chimera states has also been explored in a population exhibiting steady state dynamics, which are termed as chimera death states [52,67,68]. Like chimera state, in chimera death state the group of oscillators is subdivided into coexisting domains of coherent and incoherent steady states.…”