Emergence of extreme events in coupled systems with time-dependent interactions

Abstract

We present a class of extreme events manifested in dynamical systems involving time-dependent attractive and repulsive couplings. We consider two cases of time-varying coupling strengths -(i) explicit time-dependence (periodically varying) and (ii) implicit time dependence (distance-dependent coupling). In both of these cases, the coupled systems generate quasi-stable equilibrium points, which in turn are responsible for the generation of extreme events. In the explicit time-dependent case, the quasi-stable equilibrium points are periodically created whenever the amplitude of the external force is higher than the threshold value. In the implicit time-dependent case, they exist whenever the distance between the trajectories is below a critical distance. We demonstrate the results with the examples of two, three, and a network of hundred coupled Stuart–Landau oscillators. We also show the prevalence of this phenomenon in other dynamical systems (van der Pol oscillator) and highlight its applications in natural systems.