Dynamic interaction induced explosive death

TL;DR

This paper introduces a novel time-dependent coupling mechanism in oscillator networks, revealing how intermittent interactions can cause abrupt transitions from oscillatory to death states, with coexistence phenomena observed.

Contribution

It presents a new dynamic interaction model based on state-space proximity, demonstrating explosive transitions and coexistence of states in coupled oscillators.

Findings

Explosive transition from oscillatory to death state due to dynamic coupling.

Coexistence of oscillatory and death states over a range of coupling strengths.

Applicable to biological and technical systems for understanding sudden oscillation suppression.

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, FitzHughNagumo 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.