Bogdanov-takens singularity in tri-neuron network with time delay

Title: Bogdanov-takens singularity in tri-neuron network with time delay
Creator: He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie
Date: 2013
Type: Text; Journal article
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/62318
Identifier: vital:4960
Identifier: https://doi.org/10.1109/TNNLS.2013.2238681
Identifier: ISSN:2162-237x
Abstract: This brief reports a retarded functional differential equation modeling tri-neuron network with time delay. The Bogdanov-Takens (B-T) bifurcation is investigated by using the center manifold reduction and the normal form method. We get the versal unfolding of the norm forms at the B-T singularity and show that the model can exhibit pitchfork, Hopf, homoclinic, and double-limit cycles bifurcations. Some numerical simulations are given to support the analytic results and explore chaotic dynamics. Finally, an algorithm is given to show that chaotic tri-neuron networks can be used for encrypting a color image. © 2012 IEEE.
Relation: IEEE Transactions on Neural Networks and Learning Systems Vol. 24, no. 6 (2013), p. 1001-1007
Rights: This metadata is freely available under a CCO license
Subject: Tri-neuron network; Bogdanov-Takens bifurcations; Center manifold reductions; Chaotic dynamics; Color images; Homoclinic bifurcations; Normal form methods; Retarded functional differential equations; Bifurcation (mathematics); Neurons; Time delay; Neural networks
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