Hopf bifurcation analysis of coupled two-neuron system with discrete and distributed delays


Karaoglu E., Yilmaz E., MERDAN H.

NONLINEAR DYNAMICS, cilt.85, sa.2, ss.1039-1051, 2016 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 85 Konu: 2
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1007/s11071-016-2742-0
  • Dergi Adı: NONLINEAR DYNAMICS
  • Sayfa Sayıları: ss.1039-1051

Özet

We study the stability and Hopf bifurcation analysis of a coupled two-neuron system involving both discrete and distributed delays. First, we analyze stability of equilibrium point. Choosing delay term as a bifurcation parameter, we also show that Hopf bifurcation occurs under some conditions when the bifurcation parameter passes through a critical value. Moreover, some properties of the bifurcating periodic solutions are determined by using the center manifold theorem and the normal form theory. Finally, numerical examples are provided to support our theoretical results.