Bogdanov–Takens Singularity in Tri-Neuron Network with Time Delay Academic Article uri icon

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.

author list (cited authors)

  • He, X., Li, C., Huang, T., & Li, C.

citation count

  • 42

publication date

  • June 2013