Bifurcation, chaos and fixed-time synchronization of memristor cellular neural networks

This study investigates a novel chaotic memristive cellular neural network (CNN) and its synchronization. Firstly, a fourth-order chaotic system with a memristor is established by introducing a CNN and a memristor model. Secondly, the dynamic behavior of the system is analyzed, including its stability, bifurcation, and chaotic attractors. In particular, Hopf bifurcations are investigated in detail. Furthermore, the effects of the memristor's parameters and initial state on the dynamic behavior of the system are discussed. The conclusions are verified through the use of Lyapunov exponents and bifurcation diagrams. Additionally, the study examines the multistability that arises in memristive CNNs. Moreover, an analog electronic circuit is developed by creating appropriate system parameters to confirm the presence of chaotic attractors. Thirdly, fixed-time synchronization of memristor-based chaotic CNNs is achieved through the use of sliding mode control method. A stability criterion of error system is proposed, and the results are verified through simulation