Complex dynamics of a non-smooth temperature-sensitive memristive Wilson neuron model

Abstract

The development of neurodynamics emphasizes more accurate estimation and prediction of neuronal electrical activities in complicated physiological environments, which highlights the importance of reliable multifunctional neuronal modeling. Considering that temperature is a crucial factor in regulating the conductance and memory effect of ion channels, a non-smooth feedback strategy for temperature-dependent sodium and potassium currents is proposed. Accordingly, a Filippov-type Wilson neuron model is established to estimate the firing features of neocortical neurons under the effects of temperature and magnetic induction. The theoretical conditions for the existence and bifurcation of the equilibrium point of subsystems are clarified, further, the comb-shaped fractal structure and bistable firing modes are discovered by multiple numerical methods. The sufficient and necessary conditions of crossing, grazing, and sliding motions are presented qualitatively based on the flow switching theory. Importantly, the mechanism and evolutive rule of the self-excited and hidden sliding firing modes are revealed by employing the fast–slow analysis method. Moreover, a common approach for calculating the largest Lyapunov exponent of non-smooth systems based on Hamilton energy is designed, so that the global bifurcation patterns and multistability of the Filippov system are efficiently identified. The modeling scheme and the obtained results provide significant theoretical support for designing and optimizing intelligent systems.