Emergence of extreme events in coupled systems with time-dependent interactions
type: Item
instance of: scholarly article
title: Emergence of extreme events in coupled systems with time-dependent interactions
zbMATH Open document ID: 1496.34070
author: Suresh Kumarasamy
author: Sabarathinam Srinivasan
author: Pragjyotish Bhuyan Gogoi
author: Awadhesh Prasad
published in: Communications in Nonlinear Science and Numerical Simulation
publication date: 2022-02-04T00:00:00Z
review text: Dynamics of two or more nonlinear interacting systems being a subject of this paper is a very interesting topic. Usually a general solution to equations of motion of such a system cannot be found in symbolic form and so numerical methods are applied. In this work, the system of two Stuart-Landau (SL) oscillators in the presence of time-dependent interactions is studied and Mathematica software is used to find numerical solutions to the equations of motion for some chosen values of the system parameters. The authors consider two cases of time-varying coupling strengths. In the first case parameter determining the interactions is a periodic function of time and so the interaction depends on time explicitly. In the second case parameter determining the interactions depends on the distance or coordinates which are functions of time and so such a case is considered as ``implicit time dependence''. Note that in the first case interaction of two SL oscillators depends on the parameter $d=1+\gamma$ that is a function of time because $\gamma=f\cos (\Omega t)$. As the parameter \(d\) appears in the denominator of the term describing this interaction becomes very large for $f=0.999$ when $\cos (\Omega t)=-1$ or $\gamma=-0.999$. So it is quite natural that large amplitude oscillations may occur that are considered as extreme events, and this results are confirmed by the corresponding numerical solutions of the equations of motion. At the same time the authors introduce the ``quasi-stable equilibrium points'' a sense of which is not clear. It seems such equilibrium points are determined as solutions of the equations which are obtained if the right-hand sides of equations (3) are equated to zero. But these equations contain function of time $\gamma=f\cos (\Omega t)$ and so the corresponding ``equilibrium points'' are functions of time, as well. The question arises what is the sense of such solutions and what does it mean stability of such ``equilibrium points''? The a…
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 37C60
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 7469352
zbMATH Keywords: extreme event
zbMATH Keywords: Stuart-Landau oscillator
zbMATH Keywords: time-dependent coupling
zbMATH Keywords: distance dependent coupling
zbMATH Keywords: stability
reviewed by: A. N. Prokopenya
describes a project that uses: Mathematica
MaRDI profile type: Publication
full work available at URL: j.cnsns.2021.106170
OpenAlex ID: W4200459498
cites work: Nonlinear Dynamics in Complex Systems
cites work: Q3580272
cites work: Exploring complex networks
cites work: Mathematical biology. Vol. 1: An introduction.
cites work: Normal form analysis of stochastically forced dynamical systems
cites work: Complex networks: structure and dynamics
cites work: Oscillation quenching mechanisms: amplitude vs. oscillation death
cites work: Kuramoto model of synchronization: equilibrium and nonequilibrium aspects
cites work: A class of attractions/repulsion functions for stable swarm aggregations
cites work: Critical phenomena in natural sciences. Chaos, fractals, selforganization and disorder: Concepts and tools.
cites work: Oceanic Rogue Waves
cites work: Parametric excitation induced extreme events in MEMS and Liénard oscillator
cites work: Dynamic bifurcations. Proceedings of a conference, held in Luminy, France, March 5-10, 1990
cites work: Effect of fractional-order, time-delay and noisy parameter on slow-passage phenomenon in a nonlinear oscillator
cites work: Control of bifurcation-delay of slow passage effect by delayed self-feedback
DOI: 10.1016/J.CNSNS.2021.106170
description: scientific article; zbMATH DE number 7469352