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Bogdanov–Takens Singularity in Tri-Neuron Network With Time Delay

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4 Author(s)
Xing He ; Sch. of Electron. & Inf. Eng., Southwest Univ., Chongqing, China ; Chuandong Li ; Tingwen Huang ; Chaojie Li

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.

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Neural Networks and Learning Systems, IEEE Transactions on  (Volume:24 ,  Issue: 6 )