Memristive cyclic three-neuron-based neural network with chaos and global coexisting attractors

It has been documented that a cyclic three-neuron-based neural network with resistive synaptic weights cannot exhibit chaos. Towards this end, a memristive cyclic three-neuron-based neural network is presented using a memristive weight to substitute a resistive weight. The memristive cyclic neural network always has five equilibrium points within the parameters of interest, and their stability analysis shows that they are one index-2 saddle-focus, two index-1 saddle-foci, and two stable node-foci, respectively. Dynamical analyses are performed for the memristive cyclic neural network by several numerical simulation methods. The results demonstrate that the memristor synapse-based neural network with the simplest cyclic connection can not only exhibit chaos, but also present global coexisting attractors composed of stable points and unstable periodic or chaotic orbits under different initial conditions. Besides, with the designed implementation circuit, Multisim circuit simulations and hardware experiments are executed to validate the numerical simulations.