Hopf bifurcation analysis of a general non-linear differential equation with delay

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Atıf İçin Kopyala

Akkocaoglu H., Merdan H., Celik C.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, cilt.237, sa.1, ss.565-575, 2013 (SCI-Expanded)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 237 Sayı: 1
• Basım Tarihi: 2013
• Doi Numarası: 10.1016/j.cam.2012.06.029
• Dergi Adı: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Sayfa Sayıları: ss.565-575
• Yıldız Teknik Üniversitesi Adresli: Hayır

Özet

This work represents Hopf bifurcation analysis of a general non-linear differential equation involving time delay. A special form of this equation is the Hutchinson-Wright equation which is a mile stone in the mathematical modeling of population dynamics and mathematical biology. Taking the delay parameter as a bifurcation parameter, Hopf bifurcation analysis is studied by following the theory in the book by Hazzard et al. By analyzing the associated characteristic polynomial, we determine necessary conditions for the linear stability and Hopf bifurcation. In addition to this analysis, the direction of bifurcation, the stability and the period of a periodic solution to this equation are evaluated at a bifurcation value by using the Poincare normal form and the center manifold theorem. Finally, the theoretical results are supported by numerical simulations. (c) 2012 Elsevier B.V. All rights reserved.