Helping networks to get synchronized: Effect of external stimulation

Abstract

The attempts to evaluate the synchronizability of chaotic systems have shown that
additive periodic forcing, as a relevant source of stimuli, significantly impacts multiple forms of
synchrony. This paper investigates the complete synchronizability of coupled periodically forced
chaotic systems using the master stability function method. Three classic chaotic systems, Lorenz,
Chen’s, and Hindmarsh-Rose models are employed for this study. The numerical simulations
supporting master stability function findings are also reported. The impacts of forcing amplitude
and frequency on the critical value of coupling strength at which synchronization occurs are
determined. Evidence implies that, as the stimulation is amplified, the chaotic forced systems
tend to synchronize at weaker couplings than the autonomous versions. In contrast, high-frequency
stimulation is entirely ineffective. The required forcing amplitude is also relative to the system’s
attractor size.