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Nonuniqueness of limit cycles of Gause-type predator-prey systems. (English) Zbl 0629.34036
By comparison with the Lotka-Volterra system, we obtain a theorem concerning the nonuniqueness of limit cycles of a Gause-type predator- prey system. The method we develop here can be generalized. Moreover, we disprove a conjecture posed by H. I. Freedman by constructing an example of a system with a strictly concave down prey isocline which has at least three limit cycles.

MSC:
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
42A15 Trigonometric interpolation
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