Adaptive Intermittent Control for Fixed-Time Synchronization of Spatio-Temporal Neural Networks With Memristors

This paper analyzes the synchronization problem of cellular neural networks (CNNs) involving fuzzy min-max templates in activation functions, reaction-diffusion (RD) coefficients to represent the rate of change in space and time, the effect of time-dependent delays during the activation of neurons, and memristors with threshold conditions. Distinct to the literature works focusing on RDCNNs, this study ensures the existence of different patterns and chaotic nature in the solutions. Besides, this paper presents an analytical formula that can provide the settling time (ST) of synchronization between the controlled (response) and uncontrolled (drive) RDCNNs. This study proposes intermittent control (IC) with an adaptive mechanism to avail the dynamics of drive into response RDCNNs model. The advantage of this controller is considerably their activations updated in intervals, which may ignore the unnecessary transmissions and reduce energy consumption. Due to complex patterns in RDCNNs, this paper utilizes Lyapunov stability theory to ensure the global asymptotical stability of error dynamics between drive and response in terms of convergence to origin within a prescribed ST. This manuscript simulates and graphically demonstrates a two-neuron RDCNN model exhibiting the different patterns, which evident the performance of proposed theoretical frameworks.