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Prediction for breakup of spiral wave in a regular neuronal network

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Abstract

Target wave and spiral wave can regulate the collective behaviors of electrical activities in neuronal systems as a powerful ‘pacemaker’. Disordered states occur when normal signal propagation among neurons is disturbed and neuronal disease could be induced. In this paper, a stable rotating spiral wave is developed as initial state that the two-dimensional neuronal network of Hindmarsh–Rose neuron shows distinct periodicity and regularity in space, and then, some parameters are changed sharply to model the destruction effect induced by external large forcing or internal collapse, and the destructed areas will be expanded to occupy a larger area by expanding the damaged boundary in random way. The collapse and instability of spiral wave, ordered states could be predicated by monitoring and analyzing the time series of some nodes. It could be useful to detect the emergence of disaster in some biological or ecological systems.

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Acknowledgments

This project is partially supported by the National Natural Science of Foundation of China under Grant No. 11265008, 11365014 and also supported by the Gansu National Science of Foundation under Grant No. 1506RJZA095.

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Authors and Affiliations

  1. Department of Physics, Lanzhou University of Technology, Lanzhou, 730050, China

    Jun Ma, Ying Xu, Guodong Ren & Chunni Wang

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  1. Jun Ma
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  2. Ying Xu
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  3. Guodong Ren
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  4. Chunni Wang
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Correspondence to Jun Ma.

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Ma, J., Xu, Y., Ren, G. et al. Prediction for breakup of spiral wave in a regular neuronal network. Nonlinear Dyn 84, 497–509 (2016). https://doi.org/10.1007/s11071-015-2502-6

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  • DOI: https://doi.org/10.1007/s11071-015-2502-6

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