Continuation of solutions of coupled dynamical systems

TL;DR

This paper introduces a general model for coupled dynamical systems, proving that solutions can be extended infinitely under the QUAD condition, which is fundamental for studying synchronization.

Contribution

It proposes a unified model for coupled systems and establishes solution continuation results under the QUAD assumption.

Findings

Solutions exist on [0,+∞) under QUAD

Includes previously studied systems as special cases

Provides a foundation for synchronization analysis

Abstract

Recently, the synchronization of coupled dynamical systems has been widely studied. Synchronization is referred to as a process wherein two (or many) dynamical systems are adjusted to a common behavior as time goes to infinity, due to coupling or forcing. Therefore, before discussing synchronization, a basic problem on continuation of the solution must be solved: For given initial conditions, can the solution of coupled dynamical systems be extended to the infinite interval $[0,+\infty)$? In this paper, we propose a general model of coupled dynamical systems, which includes previously studied systems as special cases, and prove that under the assumption of QUAD, the solution of the general model exists on $[0,+\infty)$.