Spiral waves formation in a network of neuron model with monotonically differentiable magnetic flux

Spiral wave is a particular spatiotemporal pattern, observed in a wide range of complex systems such as neuronal network. Appearance of these waves is related to the network structure as well as the dynamics of its blocks. In this paper, we propose a new modified Hindmarsh-Rose neuron model. The proposed model uses a hyperbolic memductance function as the monotonically differentiable magnetic flux. An external electromagnetic excitation is also considered in the model. Firstly, we study the dynamics of the proposed neuron model through bifurcation diagram and Lyapunov spectrum, in two cases of no excitation and periodic excitation. The bifurcation diagram shows the property of antimonotonicity, which has not been observed in the previous models. Then a square network is constructed and we investigate the spatiotemporal pattrens. By varying the parameters values, spiral waves are observed in specific ranges. The formation of these waves depends on the interaction of all parameters simultaneously.