Bogdanov-Takens bifurcation in a single inertial neuron model with delay

Authors:
Xing He;Chuandong Li;Yonglu Shu
Affiliations:
College of Computer Science, Chongqing University, Chongqing 400030, PR China;College of Computer Science, Chongqing University, Chongqing 400030, PR China;College of Mathematics and Statistics, Chongqing University, Chongqing 401331, PR China
Venue:
Neurocomputing
Year:
2012

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Abstract

In this paper, we study a retarded functional differential equation modeling a single neuron with inertial term subject to time delay. Bogdanov-Takens bifurcation is investigated by using center manifold reduction and the normal form method for RFDE. We get the versal unfolding of the norm forms at the B-T singularity and show that the model can exhibit saddle-node bifurcation, pitchfork bifurcation, homoclinic bifurcation, heteroclinic bifurcation and double limit cycle bifurcation. Some numerical simulations are given to support the analytic results.