Effect of a fluctuating parameter mismatch in coupled R\"{o}ssler systems

TL;DR

This study investigates how parameter fluctuations with specific waiting times affect synchronization in coupled R"{o}ssler oscillators, revealing proportional errors and limited impact of increased coupling strength under certain fluctuation conditions.

Contribution

It introduces an analysis of the impact of fluctuating parameter mismatches with waiting times on synchronization in coupled R"{o}ssler systems, highlighting the proportional relationship and threshold effects.

Findings

Error in synchronization is proportional to waiting time and fluctuation amplitude.

Coupling strength beyond a threshold does not improve synchronization under significant fluctuations.

Parameter fluctuations with waiting times critically influence synchronization quality.

Abstract

This paper is concerned with the effect of parameter fluctuations with a characteristic waiting time in coupled R\"{o}ssler oscillators. We show that the averaged error in synchronization that is introduced due to a fluctuating parameter is proportional to the waiting time and the amplitude of the fluctuations. It is also shown that coupling strength beyond a threshold value does not have any significant effect on improving the quality of synchronization when the fluctuations posses considerable waiting time.