Hopf Bifurcation and Hybrid Control of a Delayed Ecoepidemiological Model with Nonlinear Incidence Rate and Holling Type II Functional Response

Miao Peng, Zhengdi Zhang, C. W. Lim and Xuedi Wang

Mathematical Problems in Engineering, 2018, vol. 2018, 1-12

Abstract:

Hopf bifurcation analysis of a delayed ecoepidemiological model with nonlinear incidence rate and Holling type II functional response is investigated. By analyzing the corresponding characteristic equations, the conditions for the stability and existence of Hopf bifurcation for the system are obtained. In addition, a hybrid control strategy is proposed to postpone the onset of an inherent bifurcation of the system. By utilizing normal form method and center manifold theorem, the explicit formulas that determine the direction of Hopf bifurcation and the stability of bifurcating period solutions of the controlled system are derived. Finally, some numerical simulation examples confirm that the hybrid controller is efficient in controlling Hopf bifurcation.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:6052503

DOI: 10.1155/2018/6052503

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