Transitions among the diverse oscillation quenching states induced by the interplay of direct and indirect coupling

TL;DR

This paper explores how combined direct and indirect coupling in identical oscillators induces various oscillation quenching states, including amplitude death, oscillation death, and a novel bistable state, with detailed bifurcation analysis and experimental validation.

Contribution

It introduces the first experimental evidence of multiple oscillation quenching states and their transitions caused by combined coupling schemes in oscillators.

Findings

Identification of amplitude death, oscillation death, and NAD states.

Mapping of transition scenarios in parameter space.

Experimental demonstration of these states and transitions.

Abstract

We report the transitions among different oscillation quenching states induced by the interplay of diffusive (direct) coupling and environmental (indirect) coupling in coupled identical oscillators. This coupling scheme was introduced by Resmi {\it et al}. [Phys. Rev. E, 84, 046212 (2011)] as a general scheme to induce amplitude death (AD) in nonlinear oscillators. Using a detailed bifurcation analysis we show that in addition to AD, which actually occurs only in a small region of parameter space, this coupling scheme can induce other oscillation quenching states, namely oscillation death (OD) and a novel nontrvial AD (NAD) state, which is a nonzero {\it bistable} homogeneous steady state; more importantly, this coupling mediates a transition from AD to OD state and a new transition from AD to NAD state. We identify diverse routes to the NAD state and map all the transition scenarios in the parameter space for periodic oscillators. Finally, we present the first experimental evidence of oscillation quenching states and their transitions induced by the interplay of direct and indirect coupling.