Bifurcation analysis of an autonomous epidemic predator-prey model with delay
作者： Changjin Xu , Maoxin Liao
DOI: 10.1007/S10231-012-0264-Z
关键词:
摘要: 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 center manifold theory, explicit formulas for determining direction periodic solutions derived. Some numerical simulations justifying theoretical analysis also provided. Finally, main conclusions included.
springer.com
sci-hub.se 参考文章(24)
Rui Xu, Zhien Ma, Stability and Hopf bifurcation in a ratio-dependent predator–prey system with stage structure Chaos, Solitons & Fractals. ,vol. 38, pp. 669- 684 ,(2008) , 10.1016/J.CHAOS.2007.01.019
D.V. Vayenas, G. Aggelis, V. Tsagou, S. Pavlou, Dynamics of a two-prey-one-predator system with predator switching regulated by a catabolic repression control-like mode Ecological Modelling. ,vol. 186, pp. 345- 357 ,(2005) , 10.1016/J.ECOLMODEL.2005.01.032
Xiang-Ping Yan, Cun-Hua Zhang, Hopf bifurcation in a delayed Lokta–Volterra predator–prey system Nonlinear Analysis: Real World Applications. ,vol. 9, pp. 114- 127 ,(2008) , 10.1016/J.NONRWA.2006.09.007
Bo Li, Mingxin Wang, Stationary patterns of the stage-structured predator-prey model with diffusion and cross-diffusion Mathematical and Computer Modelling. ,vol. 54, pp. 1380- 1393 ,(2011) , 10.1016/J.MCM.2011.04.007
Krishna pada Das, Kusumika Kundu, J. Chattopadhyay, A predator–prey mathematical model with both the populations affected by diseases Ecological Complexity. ,vol. 8, pp. 68- 80 ,(2011) , 10.1016/J.ECOCOM.2010.04.001
Kazuhiro Oeda, Effect of cross-diffusion on the stationary problem of a prey-predator model with a protection zone Journal of Differential Equations. ,vol. 250, pp. 3988- 4009 ,(2011) , 10.1016/J.JDE.2011.01.026
Xueyong Zhou, Xiangyun Shi, Xinyu Song, Analysis of nonautonomous predator-prey model with nonlinear diffusion and time delay Applied Mathematics and Computation. ,vol. 196, pp. 129- 136 ,(2008) , 10.1016/J.AMC.2007.05.041
Jack K. Hale, Theory of Functional Differential Equations ,(1977)
Baodan Tian, Yanhong Qiu, Ning Chen, Periodic and almost periodic solution for a non-autonomous epidemic predator-prey system with time-delay Applied Mathematics and Computation. ,vol. 215, pp. 779- 790 ,(2009) , 10.1016/J.AMC.2009.06.006
Cosme Duque, Marcos Lizana, On the dynamics of a predator–prey model with nonconstant death rate and diffusion Nonlinear Analysis-real World Applications. ,vol. 12, pp. 2198- 2210 ,(2011) , 10.1016/J.NONRWA.2011.01.002