Energy control and synchronization of thermosensitive-memristive neuron circuits

Abstract This paper embeds a thermistor and a memristor into the FitzHugh–Nagumo (FHN) neuronal circuit, and constructs a functional neuronal circuit with the capable of simultaneously perceiving temperature and electromagnetic field stimuli, which provides an effective model for gaining deeper insight into the intrinsic mechanisms of neuronal signal processing and action potential generation. The Hamilton energy of the thermosensitive-memristive neuron is calculated based on Helmholtz’s theorem, energy evolution and consumption are investigated under different discharge states, and then the energy feedback controller is utilized to control the discharge pattern. The results show that the controller not only effectively suppresses the chaotic behavior but also induces richer discharge patterns. Subsequently, an adaptive synchronization control method is adopted to explore the synchronization behavior of the neuron circuit. Since different Lyapunov functions can yield different synchronization results, the Lyapunov function in this paper is designed based on the coefficient ratios of each state variables in the Hamilton energy function. It is found that the controller and the parameter adaptive law obtained by this method can achieve drive-response synchronization. This energy regulation and adaptive synchronization strategy provides a new theoretical tool for understanding neural information coding and the cooperative control of nonlinear systems.