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Stability and Hopf bifurcation analysis for functional differential equation with distributed delay. (English) Zbl 1226.34069
Summary: The main objective of this paper is to provide some information on the stability and Hopf bifurcation analysis in a general functional differential equation with distributed delay. The local stability parameter regions related to the time delay are given and compared for a general distribution delay function and three frequently used distributed delays including Dirac, uniform and Gamma distributions. In case of loss of stability at the boundary of these regions, we discuss Hopf bifurcation by using a normal-form method. We study two examples of white blood cell models and address the effect of the distributed time delay on physiological oscillations. Numerical simulations illustrate our theoretical predictions.
MSC:
34K18Bifurcation theory of functional differential equations
34K20Stability theory of functional-differential equations
34K60Qualitative investigation and simulation of models
92C37Cell biology