Nonlinear dynamics and sliding mode control for global fixed-time synchronization of a novel 2 x 2 memristor-based cellular neural network

The paper introduces a novel 2-dimensional 2 x 2 space-invariant cellular neural network (CNN) architecture, employing a current-controlled memristor to replace the resistor in one cell's output. The CNN system is defined by space-invariant cloning templates and modeled as a fifth-order nonlinear system. Within the CNN system, non-symmetric double-wing chaotic attractors are exhibited, owing to the presence of two non-symmetric unstable equilibrium points, alongside one unstable equilibrium point located at the origin. Additionally, the paper delves into its nonlinear dynamics, ultimately determining that by adjusting the parameters of the memristor, the system exhibits chaotic and periodic attractors. Moreover, a locally sustained chaotic state is demonstrated across different initial conditions. The theoretical results are substantiated through circuit implementation. Furthermore, global fixed-time synchronization for the proposed CNN system with unmodeled dynamics and external disturbance is proposed by sliding mode control. The synchronization of the master-slave CNN system is achieved within a fixed converge time, independent on the initial conditions, and possesses a degree of robustness, as the synchronization times for CNNs with and without unmodeled dynamics and disturbances are nearly indistinguishable. The synchronization time can be manipulated by adjusting parameters of the sliding mode surface and the controller. The new discoveries pave a way for its applications to secure communications.