Open AccessDynamical characteristics of the fractional-order FitzHugh-Nagumo model neuron and its synchronization
Author(s) -
Yong Liu,
Yong Xie
Publication year - 2010
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.59.2147
Subject(s) - biological neuron model , integer (computer science) , bifurcation , order (exchange) , synchronization (alternating current) , fractional calculus , neuron , physics , mathematics , nonlinear system , computer science , topology (electrical circuits) , combinatorics , quantum mechanics , neuroscience , finance , economics , biology , programming language
Through the research on the fractional-order FitzHugh-Nagumo model neuronit is found that the Hopf bifurcation point of the fractional-order modelwhere the state of the model neuron changes from quiescence to periodic spikingis different from that of the corresponding integer-order model when the externally applied current is considered as the bifurcation parameter. We further demonstrate that the range of the strength of the externally applied current in the fractional-order model neuronwhich can make the model neuron exhibit periodic spikingis smaller than that in the corresponding integer-order model neuron. Howeverthe firing frequency of the fractional-order model neuron is higher than that of the integer-order counterpart. Meanwhilewe show that the synchronization rate of two electrically coupled fractional-order FitzHugh-Nagumo model neurons is greater than that of the integer-order counterpart. The Adomian decomposition method is employed to calculate fractional-order differential equations numerically because of its rapid convergence and high accuracy.