Solitary death in coupled limit cycle oscillators with higher-order interactions.

Abstract

Coupled limit cycle oscillators with pairwise interactions are known to depict phase transitions from an oscillatory state to amplitude or oscillation death. This Research Letter introduces a scheme to incorporate higher-order interactions which cannot be decomposed into pairwise interactions and investigates the dynamical evolution of Stuart-Landau oscillators under the impression of such a coupling. We discover an oscillator death state through a first-order (explosive) phase transition in which a single, coupling-dependent stable death state away from the origin exists in isolation without being accompanied by any other stable state usually existing for pairwise couplings. We call such a state a solitary death state. Contrary to widespread subcritical Hopf bifurcation, here we report homoclinic bifurcation as an origin of the explosive death state. Moreover, this explosive transition to the death state is preceded by a surge in amplitude and followed by a revival of the oscillations. The analytical value of the critical coupling strength for the solitary death state agrees with the simulation results. Finally, we point out the resemblance of the results with different dynamical states associated with epileptic seizures.