Hopf bifurcation in a two-competitor, one-prey system with time delay
作者： Yu Yang
DOI: 10.1016/J.AMC.2009.03.078
关键词:
摘要: In this paper, we consider a delayed two-competitor/one-prey system in which both two competitors exhibit Holling II functional response. By choosing the time delay as bifurcation parameter, it is found that Hopf occurs when passes through certain critical value. Numerical simulations are performed to illustrate analytical results.
elsevier.com
sci-hub.se 参考文章(21)
Y.-H. Wan, Nicholas D. Kazarinoff, B. D. Hassard, Theory and applications of Hopf bifurcation Cambridge University Press. ,(1981)
Shigui Ruan, Junjie Wei, On the zeros of a third degree exponential polynomial with applications to a delayed model for the control of testosterone secretion. Mathematical Medicine and Biology-a Journal of The Ima. ,vol. 18, pp. 41- 52 ,(2001) , 10.1093/IMAMMB/18.1.41
Hal L. Smith, The Interaction of Steady State and Hopf Bifurcations in a Two-Predator–One-Prey Competition Model Siam Journal on Applied Mathematics. ,vol. 42, pp. 27- 43 ,(1982) , 10.1137/0142003
Aying Wan, Junjie Wei, Bifurcation analysis in an approachable haematopoietic stem cells model Journal of Mathematical Analysis and Applications. ,vol. 345, pp. 276- 285 ,(2008) , 10.1016/J.JMAA.2008.04.014
Shigui Ruan, Ada Ardito, Paolo Ricciardi, Don L. DeAngelis, Coexistence in competition models with density-dependent mortality Comptes Rendus Biologies. ,vol. 330, pp. 845- 854 ,(2007) , 10.1016/J.CRVI.2007.10.004
Simona Muratori, Sergio Rinaldi, Remarks on competitive coexistence Siam Journal on Applied Mathematics. ,vol. 49, pp. 1462- 1479 ,(1989) , 10.1137/0149088
Junjie Wei, Shigui Ruan, Stability and bifurcation in a neural network model with two delays Physica D: Nonlinear Phenomena. ,vol. 130, pp. 255- 272 ,(1999) , 10.1016/S0167-2789(99)00009-3
Dongmei Xiao, Wenxia Li, STABILITY AND BIFURCATION IN A DELAYED RATIO-DEPENDENT PREDATOR-PREY SYSTEM Proceedings of the Edinburgh Mathematical Society. ,vol. 46, pp. 205- 220 ,(2002) , 10.1017/S0013091500001140
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
Junjie Wei, Bifurcation analysis in a scalar delay differential equation Nonlinearity. ,vol. 20, pp. 2483- 2498 ,(2007) , 10.1088/0951-7715/20/11/002