title: Bogdanov-Takens singularity in tri-neuron network with time delay.
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.
authors.forename: Xing
authors.initials: X
authors.lastname: He
authors.forename: Chuandong
authors.initials: C
authors.lastname: Li
authors.forename: Tingwen
authors.initials: T
authors.lastname: Huang
authors.forename: Chaojie
authors.initials: C
authors.lastname: Li
mesh_terms: D003198:Computer Simulation; D006801:Humans; D008433:Mathematics; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D009474:Neurons / Q000502:physiology*; D017711:Nonlinear Dynamics; D013997:Time Factors