Chaos in a Simplest Cyclic Memristive Neural Network

Previous studies have shown that cyclic neural networks which have no autoexcitation and are unidirectional cannot generate chaos. Inspired by this finding, the present paper constructs a new memristive neural network composed of three nodes connected by the simplest circular loop, whose synaptic weights are replaced by hyperbolic memristors. The memristive neural network can generate chaos via period-doubling bifurcation, and generate different stable and periodic states with the variation of parameters. Another remarkable feature of the new memristive neural network is that it coexists with point and periodic attractors, periodic and chaotic attractors from different initial conditions. Detailed dynamic analysis and circuit implementation are given to illustrate the existence of chaos and coexisting attractors, which gives a positive answer to the interesting question whether chaos can occur in neural network with the simplest cyclic connections.