Suppression and revival of oscillations through time-varying interaction

Abstract

We explore the dynamical consequences of switching the coupling form in a system of coupled oscillators. We consider two types of switching, one where the coupling function changes periodically and one where it changes probabilistically. We find, through bifurcation diagrams and Basin Stability analysis, that there exists a window in coupling strength where the oscillations get suppressed. Beyond this window, the oscillations are revived again. A similar trend emerges with respect to the relative predominance of the coupling forms, with the largest window of fixed point dynamics arising where there is balance in the probability of occurrence of the coupling forms. Further, significantly, more rapid switching of coupling forms yields large regions of oscillation suppression. Lastly, we propose an effective model for the dynamics arising from switched coupling forms and demonstrate how this model captures the basic features observed in numerical simulations and also offers an accurate estimate of the fixed point region through linear stability analysis.

Dynamics of nonlinear oscillators with time-varying conjugate coupling

“…The stability of synchronized state in time-varying networks is also explored by Kohar et al [16]. Suppression and revival of oscillations were observed by switching the coupling form in a system of coupled oscillators [17]. Moreover, the study of the spread of epidemics in timevarying networks leads to the result that if the network changes more rapidly, the disease cycle becomes more synchronized which denotes the beginning of epidemics in the system [18].…”

“…In all these existing studies, the interaction or coupling among the systems is constant over time. However, the strength or form of interaction between systems can vary with time [12][13][14][15][16][17][18][19][20]. In such cases, it is important to study the global behavior of the coupled systems which depends on the interplay between the variable strength of dynamic interaction and switching frequency between dynamic interaction strengths.…”

Emergent rhythms in coupled nonlinear oscillators due to dynamic interactions

“…The relevance of dynamic interaction has been recognized already by considering few general frameworks on the interacting nonlinear oscillators, where either the interacting function is changing over time [18][19][20][21] , or the interaction depends on the states of the individual oscillators [22][23][24] . In this article, we consider a new form of dynamic mean-field interaction with two distinct possible variations.…”

Dynamic interaction induced explosive death

“…Information diffusion over communication networks, data packet transmission on the web, disease contagion on the social network of patients are perhaps few potential examples, which attest the fundamental necessity of the temporal network approach [28,29]. Such time-varying interactions among coupled oscillators give rise to fascinating collective phenomena [30][31][32][33][34][35][36][37][38]. Earlier, Majhi et al [39] reported the emergence of death state in a temporal network of mobile oscillators.…”