Extreme Multistability with Offset Boosting of A Memristor-coupled Complex-valued Ring Network

In this paper, a non-volatile memristor is introduced to construct a complex-valued ring network (CVRN) with three laser systems. It is found that there are two groups of equilibrium points when the parameters are special. Through the analyses of the system parameter and coupling parameter by bifurcation diagram and Lyapunov exponent spectrum, it is found that system has different states, including chaos, hyperchaos, and quasi-period. It appears the coexistence of two heterogeneous attractors, including a quasi-periodic attractor and a chaotic attractor, caused by a pair of symmetric initial values. More importantly, the change of memristor initial values leads to extreme multistability with offset boosting.