Memristor initial boosting behaviors in a two-memristor-based hyperchaotic system

Abstract By substituting two resistive couplings with two memristive couplings, a two-memristor-based hyperchaotic system is proposed. This hyperchaotic system has a plane equilibrium with two zero eigenvalues and three nonzero ones, and the equilibrium plane is divided into three regions with different stabilities, including unstable saddle, stable node, and stable node-focus. Through using the local attraction basin, bifurcation diagrams and Lyapunov exponent spectra, dynamical behaviors are analyzed in the unstable saddle region, from which the bi-stability phenomenon is observed in such a hyperchaotic system. More particularly, the memristor initial boosting behaviors are found, which indicates that the attractor offset boosting is controlled by the memristor initial values. The memristor initial boosting is multi-dimension, nonlinearity and non-monotonic, completely different from the variable offset boosting. Subsequently, PSIM circuit simulations are performed to verify the numerical results.