Hopf bifurcation analysis of a general non-linear differential equation with delay |
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Authors: | Hande Akkocaoğlu Hüseyin Merdan Canan Çelik |
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Institution: | 1. TOBB University of Economics and Technology, Faculty of Science and Letters, Department of Mathematics, Sö?ütözü Cad. No 43. 06560-Ankara, Turkey;2. Bahçe?ehir University, Department of Mathematics and Computers Sciences, 34353-Istanbul, Turkey |
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Abstract: | 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 Poincaré normal form and the center manifold theorem. Finally, the theoretical results are supported by numerical simulations. |
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Keywords: | Hopf bifurcation Delay differential equation Time delay Stability Periodic solutions |
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