Dynamic analysis of a multistable memristor based coupled Wilson neuron circuits embedded in an Arduino Due microcontroller

The memristor, by reproducing the membrane potential of a first neuron before transmitting it to the next, acts as a synaptic modulator. This mechanism allows information transmission while preserving certain characteristics of the initial signal, thus providing a relevant analogy with the biological processes of synaptic plasticity. This work presents a coupled neuronal architecture based on the Wilson neuron circuits interconnected by a multistable memristor. Each neuron is modeled using two separate memristors: one simulates the sodium ion current, characterized by a fast and unstable response, while the other represents the potassium ion current, associated with a slow and stabilizing dynamic. Analysis of the system reveals steady-state stability, as well as marked dynamic diversity. In particular, the Unstable Saddle Focus (USF) fusion and disappearance mechanism, combined with the persistence of the Unstable Saddle Point (USP), promotes the emergence of cycles entering and exiting the oscillatory regime. These transitions between fast activity phases (spiking) and resting phases are characteristic of the bursting firing behaviors observed under low-frequency stimuli. Under high-frequency stimuli, the system generates complex chaotic dynamics, including transient transition behaviors, homogeneous chaotic attractors with varied amplitudes, bubble-like bifurcation, as well as multi-scroll attractors distributed in the state space. The coupled Wilson neuron model is also simulated on a digital computing device, and the results reproduce the complicated dynamic behaviors of the system including periodic bursting activities, regular and chaotic regimes.