Design, dynamic analysis, and application of a novel four-dimensional memristor-based chaotic system with hidden attractors

Abstract The research suggests a novel four-dimensional (4D) memristor-based chaotic system by adding a memristor to a 3D chaotic system with two stable equilibrium points. The associated attractors belong to hidden attractors due to the line equilibrium points of the memristor-based chaotic system. By applying nonlinear analysis tools including phase diagrams, time series diagrams and the Lyapunov exponents spectrum, these complicated dynamical behaviors and offset-boosting control of the novel system are explored, including coexisting attractors, extreme multistabilities and state transition behaviors. Furthermore, the variational approach is used to compute the unstable periodic orbits in the novel system, which are subsequently encoded using symbolic dynamics. Additionally, the active control approach is adopted to quickly accomplish synchronization of the memristor-based chaotic system. Ultimately, the digital signal processor (DSP) is used to validate the novel system, yielding noticeable experimental results that illustrate the flexibility of the proposed memristic system.