Stability and bifurcation analysis of two-neuron network with discrete and distributed delays

Karaoglu E., Yilmaz E., MERDAN H.

NEUROCOMPUTING, cilt.182, ss.102-110, 2016 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 182
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1016/j.neucom.2015.12.006
  • Dergi Adı: NEUROCOMPUTING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.102-110
  • Anahtar Kelimeler: Hopf bifurcation, Stability, Neural networks, Delay differential equations, Periodic solution, RECURRENT NEURAL-NETWORKS, HOPF-BIFURCATION, TIME DELAYS, SYSTEM, DYNAMICS, MODEL, EXISTENCE, NEURONS
  • Gazi Üniversitesi Adresli: Evet

Özet

In this paper, we give a detailed Hopf bifurcation analysis of a recurrent neural network system involving both discrete and distributed delays. Choosing the sum of the discrete delay terms as a bifurcation parameter the existence of Hopf bifurcation is demonstrated. In particular, the formulae determining the direction of the bifurcations and the stability of the bifurcating periodic solutions are studied by using the normal form theory and center manifold theorem. Finally, numerical simulations supporting our theoretical results are also included. (C) 2015 Elsevier B.V. All rights reserved.