Biriş, Larisa; Neamţu, Mihaela; Horhat, Florin R.; Opriş, Dumitru Hopf bifurcation analysis of immune response against pathogens interaction dynamics with delay kernel. (English) Zbl 1150.34013 An. Univ. Vest Timiș., Ser. Mat.-Inform. 45, No. 1, 43-57 (2007). 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 Keywords:Hopf bifurcation; delay kernel; immune response PDFBibTeX XMLCite \textit{L. Biriş} et al., An. Univ. Vest Timiș., Ser. Mat.-Inform. 45, No. 1, 43--57 (2007; Zbl 1150.34013)