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

• Huang, Tingwen

published proceedings

• IEEE Trans Neural Netw Learn Syst

author list (cited authors)

• He, X., Li, C., Huang, T., & Li, C.

citation count

• 46

complete list of authors

• He, Xing||Li, Chuandong||Huang, Tingwen||Li, Chaojie

publication date

• June 2013

publisher

• Institute of Electrical and Electronics Engineers (IEEE)  Publisher

published in

• IEEE Transactions on Neural Networks and Learning Systems  Journal

keywords

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

Digital Object Identifier (DOI)

• 10.1109/TNNLS.2013.2238681

start page

• 1001

end page

• 1007

volume

• 24

issue

• 6

URL

• http://dx.doi.org/10.1109/tnnls.2013.2238681