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Periodic solutions of delayed eco-epidemiological modelwith stage structure(PDF)


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Periodic solutions of delayed eco-epidemiological modelwith stage structure
Zhang ZizhenChu Yugui
School of Management Science and Engineering,Anhui University of Financeand Economics,Bengbu 233030,China
stage structure delay eco-epidemiological model prey predators normal form theory center manifold theorem
A delayed eco-epidemiological model with a stage structure for the prey and a transmissible disease spreading in the predator is investigated to control disease. The necessary conditions of the local stability of the positive equilibrium and the existence of a Hopf bifurcation are discussed by regarding the latent delay of the predator as the bifurcating parameter and analyzing the distribution of the roots of the associated characteristic equation. Explicit formulas determining the direction of the Hopf bifurcation and the stability of the bifurcation periodic solutions are derived by using the normal form theory and the center manifold theorem. The obtained results are verified by a numerical example.


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Last Update: 2018-12-30