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

IEEE Trans Neural Netw Learn Syst. 2013 Jun;24(6):1001-7. doi: 10.1109/TNNLS.2013.2238681.

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.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Computer Simulation*
  • Humans
  • Mathematics
  • Models, Neurological*
  • Nerve Net / physiology*
  • Neurons / physiology*
  • Nonlinear Dynamics*
  • Time Factors