Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2014, Special Issue (2014), Article ID 242410, 7 pages.
Global Hopf Bifurcation Analysis for an Avian Influenza Virus Propagation Model with Nonlinear Incidence Rate and Delay
The paper investigated an avian influenza virus propagation model with nonlinear incidence rate and delay based on SIR epidemic model. We regard delay as bifurcating parameter to study the dynamical behaviors. At first, local asymptotical stability and existence of Hopf bifurcation are studied; Hopf bifurcation occurs when time delay passes through a sequence of critical values. An explicit algorithm for determining the direction of the Hopf bifurcations and stability of the bifurcation periodic solutions is derived by applying the normal form theory and center manifold theorem. What is more, the global existence of periodic solutions is established by using a global Hopf bifurcation result.
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 242410, 7 pages.
First available in Project Euclid: 3 October 2014
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Zhai, Yanhui; Xiong, Ying; Ma, Xiaona; Bai, Haiyun. Global Hopf Bifurcation Analysis for an Avian Influenza Virus Propagation Model with Nonlinear Incidence Rate and Delay. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 242410, 7 pages. doi:10.1155/2014/242410. https://projecteuclid.org/euclid.aaa/1412360628