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economic dynamics
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.