TY - JOUR
T1 - Hopf bifurcation on a two-neuron system with distributed delays
T2 - A frequency domain approach
AU - Liao, Xiaofeng
AU - Li, Shaowen
AU - Wong, Kwok-Wo
PY - 2003/2
Y1 - 2003/2
N2 - In this paper, a more general two-neuron model with distributed delays and weak kernel is investigated. By applying the frequency domain approach and analyzing the associated characteristic equation, the existence of bifurcation parameter point is determined. Furthermore, we found that if the mean delay is used as a bifurcation parameter, Hopf bifurcation occurs for the weak kernel. This means that a family of periodic solutions bifurcates from the equilibrium when the bifurcation parameter exceeds a critical value. The direction and stability of the bifurcating periodic solutions are determine by the Nyquist criterion and the graphical Hopf bifurcation theorem. Some numerical simulations for justifying the theoretical analysis are also given.
AB - In this paper, a more general two-neuron model with distributed delays and weak kernel is investigated. By applying the frequency domain approach and analyzing the associated characteristic equation, the existence of bifurcation parameter point is determined. Furthermore, we found that if the mean delay is used as a bifurcation parameter, Hopf bifurcation occurs for the weak kernel. This means that a family of periodic solutions bifurcates from the equilibrium when the bifurcation parameter exceeds a critical value. The direction and stability of the bifurcating periodic solutions are determine by the Nyquist criterion and the graphical Hopf bifurcation theorem. Some numerical simulations for justifying the theoretical analysis are also given.
KW - Distributed delays
KW - Graphical Hopf bifurcation theorem
KW - Hopf bifurcation
KW - Neuron
KW - Nyquist criterion
KW - Periodic solutions
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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-0037305305&origin=recordpage
U2 - 10.1023/A:1022928118143
DO - 10.1023/A:1022928118143
M3 - RGC 21 - Publication in refereed journal
VL - 31
SP - 299
EP - 326
JO - Nonlinear Dynamics
JF - Nonlinear Dynamics
SN - 0924-090X
IS - 3
ER -