Bifurcation behaviors of an Euler discretized inertial delayed neuron model Academic Article

abstract

• 2016, Science China Press and Springer-Verlag Berlin Heidelberg. This paper presents an Euler discretized inertial delayed neuron model, and its bifurcation dynamical behaviors are discussed. By using the associated characteristic model, center manifold theorem and the normal form method, it is shown that the model not only undergoes codimension one (flip, Neimark-Sacker) bifurcation, but also undergoes cusp and resonance bifurcation (1:1 and 1:2) of codimension two. Further, it is found that the parity of delay has some effect on bifurcation behaviors. Finally, some numerical simulations are given to support the analytic results and explore complex dynamics, such as periodic orbits near homoclinic orbits, quasiperiodic orbits, and chaotic orbits.

authors

• Huang, Tingwen

published proceedings

• SCIENCE CHINA-TECHNOLOGICAL SCIENCES

author list (cited authors)

• He, X., Li, C., Huang, T., & Yu, J.

citation count

• 8

complete list of authors

• He, Xing||Li, ChuanDong||Huang, TingWen||Yu, JunZhi

publication date

• March 2016

publisher

• Springer Nature  Publisher

published in

• SCIENCE CHINA Technological Sciences  Journal

keywords

• Euler Discretized
• Inertial Delayed Neural Network
• Resonance Bifurcation

Digital Object Identifier (DOI)

• 10.1007/s11431-015-5986-x

start page

• 418

end page

• 427

volume

• 59

issue

• 3

URL

• http://dx.doi.org/10.1007/s11431-015-5986-x