Spiral waves in externally excited neuronal network: Solvable model with a monotonically differentiable magnetic flux

Authors: Karthikeyan Rajagopal, Fatemeh Parastesh, Hamed Azarnoush, Boshra Hatef, Sajad Jafari, Vesna Berec

Publication date: 2019

 

Journal: Chaos: An Interdisciplinary Journal of Nonlinear Science

 

Publisher: AIP Publishing

 

Description: Spiral waves are particular spatiotemporal patterns connected to specific phase singularities representing topological wave dislocations or nodes of zero amplitude, witnessed in a wide range of complex systems such as neuronal networks. The appearance of these waves is linked to the network structure as well as the diffusion dynamics of its blocks. We report a novel form of the Hindmarsh–Rose neuron model utilized as a square neuronal network, showing the remarkable multistructure of dynamical patterns ranging from characteristic spiral wave domains of spatiotemporal phase coherence to regions of hyperchaos. The proposed model comprises a hyperbolic memductance function as the monotone differentiable magnetic flux. Hindmarsh–Rose neurons with an external electromagnetic excitation are considered in three different cases: no excitation, periodic excitation, and quasiperiodic excitation. We …

 

Total citations: 35

 

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