Abstract
In this paper, a class of an autonomous epidemic predator–prey model with delay is considered. Its linear stability and Hopf bifurcation are investigated. Applying the normal form theory and center manifold theory, the explicit formulas for determining the stability and the direction of the Hopf bifurcation periodic solutions are derived. Some numerical simulations for justifying the theoretical analysis are also provided. Finally, main conclusions are included.
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This work is supported by National Natural Science Foundation of China (No. 11261010 and No. 10771215), Soft Science and Technology Program of Guizhou Province (No. 2011LKC2030), Natural Science and Technology Foundation of Guizhou Province (J[2012]2100), Governor Foundation of Guizhou Province ([2012]53) and Doctoral Foundation of Guizhou University of Finance and Economics (2010).
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Xu, C., Liao, M. Bifurcation analysis of an autonomous epidemic predator–prey model with delay. Annali di Matematica 193, 23–38 (2014). https://doi.org/10.1007/s10231-012-0264-z
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DOI: https://doi.org/10.1007/s10231-012-0264-z