Plane coexistence behaviors for Hopfield neural network with two-memristor-interconnected neurons

Memristors are commonly used as the connecting parts of neurons in brain-like neural networks. The memristors, unlike the existing literature, possess the capability to function as both self-connected synaptic weights and interconnected synaptic weights, thereby enabling the generation of intricate initials-regulated plane coexistence behaviors. To demonstrate this dynamical effect, a Hopfield neural network with two-memristor-interconnected neurons (TMIN-HNN) is proposed. On this basis, the stability distribution of the equilibrium points is analyzed, the related bifurcation behaviors are studied by utilizing some numerical simulation methods, and the plane coexistence behaviors are proved theoretically and revealed numerically. The results clarify that TMIN-HNN not only exhibits complex bifurcation behaviors, but also has initials-regulated plane coexistence behaviors. In particular, the coexistence attractors can be switched to different plane locations by the initial states of the two memristors. Finally, a digital experiment device is developed based on STM32 hardware board to verify the initials-regulated plane coexistence attractors.