Memristor synapse-coupled piecewise-linear simplified Hopfield neural network: Dynamics analysis and circuit implementation

Electromagnetic induction current is generated between the adjacent neurons in neural network caused by the existence of membrane potential difference. Memristor is the fourth fundamental electric element, which can mimic the behavior of neural synapses and simulate the electromagnetic induction effect. In this paper, in order to simplify practical implementation, the commonly used hyperbolic tangent activation function of Hopfield neural network (HNN) is replaced by a piecewise-linear function, and a simple bi-neuron-based memristor synapse-coupled HNN is proposed. Theoretical analysis and numerical simulation results illustrate that the memsirstive HNN possesses five equilibria including one unstable saddle-focus, two unstable saddle points, and two stable node points (or node-foci). Local attraction basins and phase plane plots show that the memristive HNN model behaves multistability of coexisting chaos, periodic limit cycles, and stable point attractors. Various system dynamical behaviors affected by parameters of the piecewise-linear activation function, memristor coupling strength, and initial conditions of the neurons are investigated by numerical simulations. Furthermore, an analog circuit of the memristive HNN model is simply designed, which is easier for hardware implementation as the piecewise-linear activation function can be implemented by simple op-amp-based module. Finally, the experimental results verify the correctness of the design and analyses.