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August  2005, 5(3): 841-860. doi: 10.3934/dcdsb.2005.5.841

Discrete May-Leonard competition models II

Lih-Ing W. Roeger 1,

1. 

Department of Mathematics and Statistics, Box 41042, Texas Tech University, Lubbock, TX 79409-1042, United States

Received  December 2002 Revised  March 2005 Published  May 2005

We analyzed the local dynamics of a three-dimensional Ricker type discrete-time competition model that is analogous to the May-Leonard (M-L) differential equation model. The symmetric discrete M-L model is mentioned by Hofbauer et al. [[7] J. Math. Biol., 25:553--570,1987] as "perhaps one of the most difficult three species problems''. Both of the discrete and the continuous M-L models have similar local dynamics. However, the discrete model is not dynamically consistent with the continuous model. Unlike the continuous M-L model, the discrete Hopf bifurcations (Neimark-Sacker bifurcations) of the discrete M-L model are not degenerate. The continuous M-L model is the limiting case of the discrete model.
Keywords: May-Leonard systems, Hopf bifurcation., Neimark-Sacker bifurcation.
Mathematics Subject Classification: Primary: 39A1.
Citation: Lih-Ing W. Roeger. Discrete May-Leonard competition models II. Discrete & Continuous Dynamical Systems - B, 2005, 5 (3) : 841-860. doi: 10.3934/dcdsb.2005.5.841
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