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-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 85 Sayı: 2
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1007/s11071-016-2742-0
  • Dergi Adı: NONLINEAR DYNAMICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1039-1051
  • Anahtar Kelimeler: Hopf bifurcation, Stability, Neural network, Delay, Periodic solution, RECURRENT NEURAL-NETWORKS, STABILITY ANALYSIS, TIME DELAYS, DYNAMICS, NEURONS, MODEL, EXISTENCE, AUTAPSES
  • Gazi Üniversitesi Adresli: Evet

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.