Dynamic interaction induced explosive death

¹ Department of Physics, Central University of Rajasthan - NH-8, Bandar Sindri, Ajmer 305 817, India
² Physics and Applied Mathematics Unit, Indian Statistical Institute - 203 B. T. Road, Kolkata 700108, India

^(a) shrimali@curaj.ac.in

Received: 4 December 2020
Accepted: 18 January 2021

Abstract

Most previous studies on coupled dynamical systems assume that all interactions between oscillators take place uniformly in time, but, in reality, this does not necessarily reflect the usual scenario. The heterogeneity in the timings of such interactions strongly influences the dynamical processes. Here, we introduce a time-evolving state-space-dependent coupling among an ensemble of identical coupled oscillators, where individual units are interacting only when the mean state of the system lies within a certain proximity of the phase space. They interact globally with mean-field diffusive coupling in a certain vicinity and behave like uncoupled oscillators with self-feedback in the remaining complementary subspace. Interestingly due to this occasional interaction, we find that the system shows an abrupt explosive transition from oscillatory to death state. Further, in the explosive death transitions, the oscillatory state and the death state coexist over a range of coupling strengths near the transition point. We explore our claim using Van der Pol, FitzHugh-Nagumo and Lorenz oscillators with dynamic mean field interaction. The dynamic interaction mechanism can explain sudden suppression of oscillations and concurrence of oscillatory and steady state in biological as well as technical systems.