A new multistable chaotic system with memristor and memcapacitor for fractional-order: dynamical analysis, implementation, and synchronization

In this paper, a new multistable chaotic system with memristor and memcapacitor for fractional-order is constructed. A chaotic oscillator of parallel memcapacitor and memristor is designed, the system for fractional-order can be obtained. Then equilibrium point stability of the system is analyzed. The dynamical behavior of order and parameter is analyzed. Interestingly, special dynamical behavior state transfer is found. In addition, the multistability is found with the different initial values. The digital circuit is implemented on the DSP platform that verify the feasibility of the system. Finally, the synchronization controller is designed based on fractional Lyapunov stability theory and its synchronization is investigated. The results show that it has rich dynamical behaviors. It provides a reference for application in confidential communication.