Two-memristor-based chaotic system and its extreme multistability reconstitution via dimensionality reduction analysis

Abstract This paper presents a two-memristor-based chaotic system by introducing two memristors into an existing chaotic jerk system. Such a memristive system possesses plane equilibrium therein, leading to the emergence of extreme multistability. Due to the existence of two zero eigenvalues for the plane equilibrium, it is extremely difficult to quantitatively explore the dynamical mechanism based on the original system model. For this reason, an equivalent dimensionality reduction model is obtained using state variable mapping (SVM) method. Consequently, the initials-dependent extreme multistability in the two-memristor-based chaotic system is reconstituted by the initial parameters-related dynamics in the dimensionality reduction model, upon which the exact prediction, analysis and control of extreme multistability is thereby executed through traditional quantitative analyses. Furthermore, PSIM circuit simulations based on a physical circuit are performed to confirm the extreme multistability. It is demonstrated that the initials-dependent extreme multistability can be reconstituted through dimensionality reduction analysis, which is efficient for exploring the inner mechanisms and further seeking possible applications of this special phenomenon.