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

Communications in Nonlinear Science and Numerical Simulation. 2022. Vol. 107. Article 106170.

Kumarasamy S., Srinivasan S., Gogoi P. B., Prasad A.

We present a class of extreme events manifested in dynamical systems involving time-dependentattractive  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 equilibriumpoints,  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 amplitudeof the external force is higher than the threshold value.  In the implicit time-dependent case, theyexist whenever the distance between the trajectories is below a critical distance. We demonstrate theresults 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.

Keywords: complex networks, methods: numerical, Complex System Analysis

Publication based on the results of: Data analysis and modeling of the structure and dynamics of plasma formations and processes in the solar system responsible for solar-terrestrial communications and processes on Earth (2022)