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Critical values of stability and Hopf bifurcations for a delayed population model with delay-dependent parameters. (English) Zbl 1190.34106
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 τ 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.
34K60Qualitative investigation and simulation of models
34K18Bifurcation theory of functional differential equations
34K20Stability theory of functional-differential equations
92D25Population dynamics (general)
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