Spatiotemporal pattern in a neural network with non-smooth memristor

Considering complicated dynamics of non-smooth memductance function, an improved Hindmarsh-Rose neuron model is introduced by coupling with non-smooth memristor and dynamics of the improved model are discussed. Simulation results suggest that dynamics of the proposed neuron model depends on the external stimuli but not on the initial value for the magnetic flux. Furthermore, a network composed of the improved Hindmarsh-Rose neuron is addressed via single channel coupling method and spatiotemporal patterns of the network are investigated via numerical simulations with no-flux boundary condition. Firstly, development of spiral wave are discussed for different coupling strengths, different external stimuli and various initial value for the magnetic flux. Results suggest that spiral wave can be developed for coupling strength $0<D<1$ when the nodes are provided with period-1 dynamics, especially, double-arm spiral wave appear for $D=0.4$.External stimuli changing can make spiral wave collapse and the network demonstrates chaotic state. Alternation of initial value for the magnetic flux hardly has effect on the developed spiral wave. Secondly, formation of target wave are studied for different coupling strengths, different sizes of center area with parameter diversity and various initial value for the magnetic flux. It can be obtained that, for certain size of center area with parameter diversity, target wave can be formed for coupling strength $0<D<1$, while for too small size of center area with parameter diversity, target wave can hardly be formed. Change of initial value for the magnetic flux has no effect on the formation of target wave. Research results reveal the spatiotemporal patterns of neuron network to some extent and may provide some suggestions for exploring some disease of neural system.