Displaying similar documents to “Periodic dynamics in a model of immune system”

Global Existence of Periodic Solutions in a Delayed Tumor-Immune Model

A. Kaddar, H. Talibi Alaoui (2010)

Mathematical Modelling of Natural Phenomena

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This paper is devoted to the study of global existence of periodic solutions of a delayed tumor-immune competition model. Also some numerical simulations are given to illustrate the theoretical results

Dynamical behavior of Volterra model with mutual interference concerning IPM

Yujuan Zhang, Bing Liu, Lansun Chen (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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A Volterra model with mutual interference concerning integrated pest management is proposed and analyzed. By using Floquet theorem and small amplitude perturbation method and comparison theorem, we show the existence of a globally asymptotically stable pest-eradication periodic solution. Further, we prove that when the stability of pest-eradication periodic solution is lost, the system is permanent and there exists a locally stable positive periodic solution which arises from the pest-eradication...

An epidemic model with a time delay in transmission

Q. J. A. Khan, E. V. Krishnan (2003)

Applications of Mathematics

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We study a mathematical model which was originally suggested by Greenhalgh and Das and takes into account the delay in the recruitment of infected persons. The stability of the equilibria are also discussed. In addition, we show that the introduction of a time delay in the transmission term can destabilize the system and periodic solutions can arise by Hopf bifurcation.

Hybrid matrix models and their population dynamic consequences

Sanyi Tang (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper, the main purpose is to reveal what kind of qualitative dynamical changes a continuous age-structured model may undergo as continuous reproduction is replaced with an annual birth pulse. Using the discrete dynamical system determined by the stroboscopic map we obtain an exact periodic solution of system with density-dependent fertility and obtain the threshold conditions for its stability. We also present formal proofs of the supercritical flip bifurcation at the bifurcation...