Hopf-pitchfork bifurcation in an inertial two-neuron system with time delay

abstract

• In this paper, we have considered a delayed differential equation modeling two-neuron system with both inertial terms and time delay. By studying the distribution of the eigenvalues of the corresponding transcendental characteristic equation of the linearization of this equation, we derive the critical values where Hopf-pitchfork bifurcation occurs. Then, by computing the normal forms for the system, the bifurcation diagrams are obtained. Furthermore, we find some interesting phenomena, such as the coexistence of two asymptotically stable states, two stable periodic orbits, and two attractive quasi-periodic motions, which are verified both theoretically and numerically. 2012 Elsevier B.V.

authors

• Huang, Tingwen

published proceedings

• NEUROCOMPUTING

author list (cited authors)

• Dong, T., Liao, X., Huang, T., & Li, H.

citation count

• 34

complete list of authors

• Dong, Tao||Liao, Xiaofeng||Huang, Tingwen||Li, Huaqing

publication date

• November 2012

publisher

• Elsevier  Publisher

published in

• Neurocomputing  Journal

keywords

• Hopf-pitchfork Bifurcation
• Inertial
• Time Delay
• Two-neuron System

Digital Object Identifier (DOI)

• 10.1016/j.neucom.2012.06.008

start page

• 223

end page

• 232

volume

• 97

URL

• http%3A%2F%2Fdx.doi.org%2F10.1016%2Fj.neucom.2012.06.008