Abstract
In this paper, the dynamical behavior of an eco-epidemiological model with discrete and distributed delay is studied. Sufficient conditions for the local asymptotical stability of the nonnegative equilibria are obtained. We prove that there exists a threshold value of the feedback time delay τ beyond which the positive equilibrium bifurcates towards a periodic solution. Using the normal form theory and center manifold argument, the explicit formulae which determine the stability, the direction and the periodic of bifurcating period solutions are derived. Numerical simulations are carried out to explain the mathematical conclusions.
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This work is supported by the National Natural Science Foundation of China (No. 10771179), the Henan Innovation Project for University Prominent Research Talents (No. 2005KYCX017) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.
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Shi, X., Zhou, X. & Song, X. Dynamical behavior for an eco-epidemiological model with discrete and distributed delay. J. Appl. Math. Comput. 33, 305–325 (2010). https://doi.org/10.1007/s12190-009-0288-8
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DOI: https://doi.org/10.1007/s12190-009-0288-8