caa a22 4500 445361417 CHVBK 20180317142916.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s11071-010-9881-5 doi (NATIONALLICENCE)springer-10.1007/s11071-010-9881-5 Hopf and Bogdanov-Takens bifurcations in a coupled FitzHugh-Nagumo neural system with delay [Elektronische Daten] [Yanqiu Li, Weihua Jiang] In this paper, Hopf bifurcation and Bogdanov-Takens bifurcation with codimension 2 in a coupled FitzHugh-Nagumo neural system with gap junction are investigated. At first, a general bifurcation diagram on the plane of coupling strength and delay is derived. Then, explicit algorithms due to Hassard and Faria are applied to determine the normal forms of Hopf and Bogdanov-Takens bifurcations, respectively. Next, we analyze the codimension-2 unfolding for Bogdanov-Takens bifurcation, and give complete bifurcation diagrams and phase portraits. Furthermore, we also consider the spatio-temporal patterns of bifurcating periodic solutions by using the symmetric bifurcation theory of delay differential equations combined with representation theory of Lie groups. By the results of theoretical analysis, we obtain that the values of coupled strength, which make the transmission and received signals be synchronous and anti-phase, are opposite. And universal unfolding of Bogdanov-Takens bifurcation indicates that the neuron signals can transit between resting and spiking. Springer Science+Business Media B.V., 2010 FitzHugh-Nagumo neural model nationallicence Time delay nationallicence Hopf bifurcation nationallicence Bogdanov-Takens bifurcation nationallicence Normal form nationallicence Li Yanqiu Department of Mathematics, Harbin Institute of Technology, 150001, Harbin, China aut Jiang Weihua Department of Mathematics, Harbin Institute of Technology, 150001, Harbin, China aut Nonlinear Dynamics Springer Netherlands 65/1-2(2011-07-01), 161-173 0924-090X 65:1-2<161 2011 65 11071 https://doi.org/10.1007/s11071-010-9881-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11071-010-9881-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Li Yanqiu Department of Mathematics, Harbin Institute of Technology, 150001, Harbin, China aut NATIONALLICENCE 700 1- Jiang Weihua Department of Mathematics, Harbin Institute of Technology, 150001, Harbin, China aut NATIONALLICENCE 773 0- Nonlinear Dynamics Springer Netherlands 65/1-2(2011-07-01), 161-173 0924-090X 65:1-2<161 2011 65 11071 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer