Bias and rotation control of FHN neuron coupled with locally active memristor

Abstract This paper focuses on the FitzHugh-Nagumo (FHN) neuron system. We construct a three-dimensional memristive neuron system by introducing an exponential locally active memristor. The bias control of neurons is achieved by introducing bias constant terms or periodic functions into the system. Moreover, trigonometric functions and absolute value functions are used to respectively realize the self-replication and symmetrization of attractors as well as other regulations of multi-stable dynamic states. The initial conditions also exert an influence on the bias control of neurons. Meanwhile, we introduce a three-dimensional matrix rotating around the z-axis to implement rotation control. Analysis reveals that as the rotation angle θ varies from 0 to 2 π , the offset of the neuron membrane potential undergoes periodic variations. Rotation control can alter the arrangement of attractors and enhance the performance of the neural network. The research findings offer a theoretical basis for understanding the dynamic behavior of neurons and developing new neural network models and hold potential value for assisting in the diagnosis of nervous system diseases.