Synchronization and different patterns in a network of diffusively coupled elegant Wang–Zhang–Bao circuits

Abstract

Synchronization in coupled oscillators is of high importance in secure communication and information processing. Due to this reason, a significant number of studies have been performed to investigate the synchronization state in coupled circuits. Diffusive coupling is the simplest connection between the oscillators, which can be implemented through a variable resistor between two variables of two circuits. The Chua’s circuit is the most famous chaotic circuit whose dynamics have been investigated in many studies. However, Wang–Zhang–Bao (WZB) is another chaotic circuit that can exhibit exciting behaviors such as bistability. Thus, this study aims to investigate the cooperative dynamics of the WZB circuit in its elegant parameter values. To this issue, first, we explored the dynamic behavior of the elegant WZB circuit using the bifurcation diagrams, the Lyapunov exponents, and the basins of attraction. Based on the results, we found the range of the bifurcation parameter and the initial conditions wherein the system is bistable. Subsequently, setting the parameters in the monostable region, we studied the synchronization state of two diffusively coupled WZB circuits analytically and numerically. Consequently, we used master stability functions and temporally averaged synchronization error as the analytical and numerical tools to explore the synchronization state. Then we numerically examined the synchronization state in a network of 100 nonlocally coupled WZB oscillators. As a result, we found imperfect chimera and phase synchronization in the studied network before getting synchronized.