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Hopf bifurcation analysis of immune response against pathogens interaction dynamics with delay kernel. (English) Zbl 1150.34013

Summary: The aim of this paper is to study the steady states of the mathematical models with delay kernels which describe pathogen-immune dynamics of many kinds of infections diseases. By using the coeffient of kernel \(k\), as a bifurcation parameter, the models are found to undergo a sequence of Hopf bifurcation. The direction and the stability criteria of bifurcation periodic solutions are obtained by applying the normal form theory and the center manifold theorems. The numerical simulation that we did justifies the theoretical results.

MSC:

34C23 Bifurcation theory for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
37G05 Normal forms for dynamical systems
37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
47N60 Applications of operator theory in chemistry and life sciences
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