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Simulating the formation of spiral wave in the neuronal system

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Abstract

Some experimental results have confirmed that a spiral wave could be observed in the cortex of brain. The biological Hodgkin–Huxley neurons are used to construct a regular network with nearest-neighbor connection, artificial line defects are generated to block the traveling wave in the network, and the potential mechanism for formation of spiral wave is investigated. A target wave is generated in a local area by imposing two external forcing currents with diversity (I 0I 1) in different areas of the network. It is confirmed that spiral wave could be induced by the defects even if no specific initial values are used. A single perfect spiral wave can occupy the network when the coupling intensity exceeds certain threshold; otherwise, a group of spiral waves emerges in the network. Certain channel noise can enhance the diversity (I 0I 1) for generating target wave, and then spiral waves are induced by blocking the target wave with defects under no-flux and/or periodic boundary conditions in the network.

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Acknowledgements

This work is partially supported by the National Natural Science Foundation of China under Grant No. 11265008.

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Correspondence to Jun Ma.

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Ma, J., Hu, B., Wang, C. et al. Simulating the formation of spiral wave in the neuronal system. Nonlinear Dyn 73, 73–83 (2013) doi:10.1007/s11071-013-0767-1

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Keywords

  • Target wave
  • Spiral wave
  • Defects
  • Network
  • Factor of synchronization