Stability of limit cycle in a delayed model for tumor immune system competition with negative immune response

Yafia, Radouane

doi:https://doi.org/10.1155/DDNS/2006/58463

Discrete Dynamics in Nature and Society

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Volume 2006 | Article ID 058463 | https://doi.org/10.1155/DDNS/2006/58463

Stability of limit cycle in a delayed model for tumor immune system competition with negative immune response

Radouane Yafia¹

Received20 Dec 2005

Accepted11 Apr 2006

Published10 Jul 2006

Abstract

This paper is devoted to the study of the stability of limit cycles of a system of nonlinear delay differential equations with a discrete delay. The system arises from a model of population dynamics describing the competition between tumor and immune system with negative immune response. We study the local asymptotic stability of the unique nontrivial equilibrium of the delay equation and we show that its stability can be lost through a Hopf bifurcation. We establish an explicit algorithm for determining the direction of the Hopf bifurcation and the stability or instability of the bifurcating branch of periodic solutions, using the methods presented by Diekmann et al.

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Copyright

Copyright © 2006 Radouane Yafia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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