With a magnetically controlled memristor to describe the coupling between membrane potential and magnetic flux, a magnetic induction HR neuron model is established. Its complex dynamical behavior is revealed with dynamic analysis methods including bifurcation diagrams, Lyapunov exponent spectrum, time sequences, and phase plots. It shows that the magnetic induction HR neuron has no equilibrium points while it can generate infinite hidden chaotic attractors with same topologies and different positions. Namely, the neuron model has the characteristic of hidden extreme multistability. Moreover, an analog equivalent circuit of the magnetic induction HR neuron is designed. Numerical simulations is verified with PSIM circuit simulations.

An extremely multistable memristive Hopfield neural network (HNN) is proposed which includes only three neurons and one multistable memristor synapse. Dissipativity and stability of equilibrium points are theoretically analyzed, and influence of memristive synapse-coupled strengths on dynamics in the memristive neural network is analyzed with numerical methods such as bifurcation diagrams, Lyapunov exponents, and phase plots. As network parameters are fixed, dynamical behavior of extreme multistability related to initial states is revealed. Finally, analog equivalent circuit of the memristive HNN is designed, and MATLAB numerical simulation results are verified with PSIM circuit simulation.