Complex dynamics and autapse-modulated information patterns in memristive Wilson neurons

This paper introduces and investigates the dynamics of an improved Wilson neuron model with a memristive autapse. The study of the stability of the equilibrium points of the proposed model revealed that it can move from a rest state to a firing state through a Hopf bifurcation. Therefore, the improved model experiences self-excited dynamics. The study of the dynamics of the proposed model revealed neuronal behaviors such as quiescent, bursting, spiking, and hysteretic dynamics characterized by the coexistence of two and three firing patterns for the same set of parameters. In addition, the dynamics of modulated information patterns via the membrane potential related to potential information coding in a network of 500 neurons are presented and discussed. Planar impulse wave solutions of the generic model as initial conditions result in a localized unstable wave pattern under autaptic coupling and magnetic flux time delay. High memristive autaptic coupling and magnetic flux time delay have antagonistic effects on the spatiotemporal patterns. Our results suggest that high autaptic coupling could be a possible route to chaotic and chimera-like behaviors in the network, while high magnetic flux time delay could be an efficient bifurcation parameter in controlling the chaotic and chimera-like behaviors. Finally, a microcontroller implementation of the introduced memristive Wilson neuron has been addressed based on the 32-bit STM 32 F 407 ZE development board. Results obtained from the experimental investigations of the model agreed with the numerical ones based on the physically captured phase trajectories and time-domain waveforms.