Abstract
Memristive system with infinitely many equilibrium points has attracted much attention for the generation of extreme multistability, whose initial-dependent dynamics can be interpreted in a reduced-order model through incremental integral transformation of state variables. But, the memristive system with any extra nonlinear terms besides the memristor ones cannot be handled directly using this method. In addition, the transformed state variables could be divergent due to the asymmetry of the original system. To solve these problems, a hybrid state variable incremental integral (HSVII) method is proposed in this paper. With this method, the extreme multistability in a four-dimensional (4D) memristive jerk system with cubic nonlinearity is successfully reconstituted in a three-dimensional (3D) model and the divergent state variables are eliminated through ingenious linear state variable mapping. Thus, mechanism analysis and physical control of the special extreme multistability can readily be performed. A hardware circuit is finally designed and fabricated, and the theoretical and numerical results are verified by the experimental measurements. It is demonstrated that this HSVII method is effective for the analysis of multistable system with high-order nonlinearities.
Highlights
Initial-dependent multistability [1,2,3,4,5] phenomenon is an intrinsic phenomenon of nonlinear dynamical systems, which provides great flexibility or crisis [6,7,8,9] for seeking potential uses in chaos-based engineering applications
When the initial values are considered during the integration of voltage and current, the initial states of all dynamic elements can be expressed as standalone system parameters [28, 29] and the initial-dependent dynamics of the original memristive circuit can be reflected in the flux-charge domain
A 4D memristive jerk system is present, which is obtained by introducing an ideal memristor into a 3D chaotic jerk system
Summary
Initial-dependent multistability [1,2,3,4,5] phenomenon is an intrinsic phenomenon of nonlinear dynamical systems, which provides great flexibility or crisis [6,7,8,9] for seeking potential uses in chaos-based engineering applications. When the initial values are considered during the integration of voltage and current, the initial states of all dynamic elements can be expressed as standalone system parameters [28, 29] and the initial-dependent dynamics of the original memristive circuit can be reflected in the flux-charge domain With this improvement, the incremental flux-charge analysis method can readily be applied for the investigations of Complexity relative complex memristive circuits [30], e.g., the memristive cellular neural networks [31] and arrays of memristor oscillators [32]. In the second step, the difference of the first and fourth state variables is chosen as a new state variable Through this linear transformation, the divergence is eliminated and a 3D reduced-order model is obtained, which facilitates mechanism analyses and physical measurements of the original initial-dependent dynamics.
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