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Zbl 1190.34106
Fan, Li; Shi, Zhongke; Tang, Sanyi
Critical values of stability and Hopf bifurcations for a delayed population model with delay-dependent parameters. (English)
[J] Nonlinear Anal., Real World Appl. 11, No. 1, 341-355 (2010). ISSN 1468-1218

The authors consider a delayed population model with delay-dependent parameters. They prove analytically that the positive equilibrium switches from being stable to unstable and then back to stable as the delay $\tau$ increases, and Hopf bifurcations occur between the two critical values of stability changes. The critical values for the stability switches and Hopf bifurcations can be analytically determined. Using the perturbation approach and Floquet technique, they also obtain an approximation to the bifurcating periodic solution and derive formulas for determining the direction and stability of the Hopf bifurcations. Finally, they illustrate their results by some numerical examples.
[Fuhua Ling (Milpitas)]

MSC 2000:: *34K60 Applications of functional-differential equations
34K18 Bifurcation theory of functional differential equations
34K20 Stability theory of functional-differential equations
92D25 Population dynamics

Keywords: delay differential equations; Hopf bifurcation; stability switch; perturbation approach

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