Abstract
Neurons in the brain are interconnected through synapses. Local active memristors can both simulate the synaptic behavior of neurons and the action potentials of neurons. Currently, the hyperbolic tangent function-type memristors used for coupling neural networks do not belong to local active memristors. To take advantage of local active memristors and consider the multi-equilibrium point problem, a cosine function is introduced into the state equation, resulting in the design of an absolute value hyperbolic tangent-type double local active memristor, and it is used as a coupling synapse to replace a synaptic weight in a 3-neuron HNN. Then, basic dynamical analysis methods are used to study the effects of different memristor synapse coupling strengths and different initial conditions on the dynamics of the neural network. The research results indicate that dynamical behavior of memristor Hopfield neural network is closely related to the synaptic coupling strengths and the initial conditions, and this neural network exhibits rich dynamical behaviors, including the coexistence of chaotic and periodic attractors, super-multistability phenomena, etc. Finally, the neural network was implemented using an FPGA development board, verifying the hardware feasibility of this system.