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Dynamical behavior and network analysis of an extended Hindmarsh–Rose neuron model

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Abstract

In this paper, the extended Hindmarsh–Rose neuron model, which considers the slow intracellular exchange of calcium ions between its store and the cytoplasm, is studied. The dynamical behavior of this neuron model is analyzed by deriving the equilibrium points, the bifurcation diagrams, and the Lyapunov exponents, in the presence of an external forcing current. Furthermore, the dynamics of the network of the extended model is investigated. Firstly, a one-dimensional ring network is constructed, and the effects of the coupling strength and the forcing current are considered on the network behavior. The results confirm the existence of chimera state in small coupling strength values. Then, a square network of the proposed model is created by adding an external excitation to the neurons and four cases of different parameters are considered. Particularly, the effects of the stimulus parameters, the external current, and the coupling strength are studied on the emergence of spiral waves.

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Authors and Affiliations

  1. Center for Nonlinear Dynamics, Institute of Research and Development, Defence University, Bishoftu, Ethiopia

    Karthikeyan Rajagopal & Anitha Karthikeyan

  2. Institute of Energy, Mekelle University, Mekelle, Ethiopia

    Karthikeyan Rajagopal

  3. Ministry of Higher Education and Scientific Research, Baghdad, Iraq

    Abdul Jalil M. Khalaf

  4. Department of Biomedical Engineering, Amirkabir University of Technology, Tehran, Iran

    Fatemeh Parastesh

  5. Mathematical Institute, University of Oxford, Andrew Wiles Building, Oxford, UK

    Irene Moroz

  6. Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Sajad Jafari

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  1. Karthikeyan Rajagopal
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  2. Abdul Jalil M. Khalaf
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  3. Fatemeh Parastesh
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Correspondence to Sajad Jafari.

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Rajagopal, K., Khalaf, A.J.M., Parastesh, F. et al. Dynamical behavior and network analysis of an extended Hindmarsh–Rose neuron model. Nonlinear Dyn 98, 477–487 (2019). https://doi.org/10.1007/s11071-019-05205-0

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  • DOI: https://doi.org/10.1007/s11071-019-05205-0

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