Emergent rhythms in coupled nonlinear oscillators due to dynamic interactions

TL;DR

This paper investigates how dynamic interactions in networks of identical oscillators lead to various complex states, including synchronization, oscillation death, and bistability, with transitions characterized by numerical and analytical methods.

Contribution

It introduces a novel dynamic coupling mechanism that induces diverse asymptotic states and analyzes the nature of phase transitions depending on initial conditions.

Findings

Dynamic coupling facilitates multiple asymptotic states.

Transitions can be first or second order depending on initial conditions.

Results extend to chaotic and ecological models.

Abstract

The role of a new form of dynamic interaction is explored in a network of generic identical oscillators. The proposed design of dynamic coupling facilitates the onset of a plethora of asymptotic states including synchronous states, amplitude death states, oscillation death states, a mixed state (complete synchronized cluster and small amplitude unsynchronized domain), and bistable states (coexistence of two attractors). The dynamical transitions from the oscillatory to death state are characterized using an average temporal interaction approximation, which agrees with the numerical results in temporal interaction. A first-order phase transition behavior may change into a second-order transition in spatial dynamic interaction solely depending on the choice of initial conditions in the bistable regime. However, this possible abrupt first-order like transition is completely non-existent in the case of temporal dynamic interaction. Besides the study on periodic Stuart-Landau systems, we present results for paradigmatic chaotic model of R\"ossler oscillators and Mac-arthur ecological model.