The effect of nonlinear diffusive coupling on the synchronization of coupled oscillators

Abstract

This paper examines the impact of nonlinear coupling on the synchronization of interconnected oscillators. Various powers of diffusive coupling are explored to introduce nonlinear effects, and the results are contrasted with those of linear diffusive coupling. The study employs three representative chaoic systems—namely, the Lorenz, R¨ossler, and Hindmarsh-Rose systems. Findings indicate that nonlinear couplings with power below one result in synchronization at lower coupling strengths. Additionally, the critical coupling strength reduces as the coupling power decreases. However, the synchronization region undergoes changes and becomes bounded.
Conversely, for powers exceeding one, networks are either unable to synchronize or require higher coupling strengths compared to linear coupling.