Abstract
The phase transition of spiral waves in networks of Hodgkin-Huxley neurons induced by channel noise is investigated in detail. All neurons in the networks are coupled with small-world connections, and the results are compared with the case for regular networks, in which all neurons are completely coupled with nearest-neighbor connections. A statistical variable is defined to study the collective behavior and phase transition of the spiral wave due to the channel noise and topology of the network. The effect of small-world connection networks is described by local regular networks and long-range connection with certain probability p. The numerical results confirm that (1) a stable rotating spiral wave can be developed and maintain robust with low p, where the breakup of the spiral wave and turbulence result from increasing the probability p to a certain threshold; (2) appropriate intensity of the optimized channel noise can develop a spiral wave among turbulent states in small-world connection networks of H-H neurons; and (3) regular connection networks are more robust to channel noise than small-world connection networks. A spiral wave in a small-world network encounters instability more easily as the membrane temperature is increased to a certain high threshold.
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Ma, J., Wu, Y., Ying, H. et al. Channel noise-induced phase transition of spiral wave in networks of Hodgkin-Huxley neurons. Chin. Sci. Bull. 56, 151–157 (2011). https://doi.org/10.1007/s11434-010-4281-2
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DOI: https://doi.org/10.1007/s11434-010-4281-2