Channel noise-induced phase transition of spiral wave in networks of Hodgkin-Huxley neurons

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.