Codimension two bifurcation in a simple delayed neuron model

abstract

• This paper reports a simple delayed neuron model. Bogdanov-Takens bifurcation is studied by using the center manifold reduction and the normal form method for retarded functional differential equation. We get the versal unfolding of the norm forms at double zero singularity and show that the model can exhibit pitchfork, Hopf, homoclinic bifurcation and saddle node bifurcation of periodic orbits. Some numerical simulations are given to support the analytic results. 2012 Springer-Verlag London Limited.

authors

• Huang, Tingwen

published proceedings

• NEURAL COMPUTING & APPLICATIONS

author list (cited authors)

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

citation count

• 14

complete list of authors

• He, Xing||Li, Chuandong||Huang, Tingwen||Peng, Mei

publication date

• December 2013

publisher

• Springer Nature  Publisher

published in

• Neural Computing and Applications  Journal

keywords

• Codimension Two Bifurcation
• Delayed Neuron Model
• Homoclinic Bifurcation
• Saddle Node Bifurcation Of Periodic Orbits

Digital Object Identifier (DOI)

• 10.1007/s00521-012-1181-1

start page

• 2295

end page

• 2300

volume

• 23

issue

• 7-8

URL

• http://dx.doi.org/10.1007/s00521-012-1181-1