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Uniqueness of limit cycles of generalised Liénard systems and predator- prey systems. (English) Zbl 0661.34028
In this letter, another interesting example of how mathematical methods in physics can be applied to the area of ecology is presented. By using a theorem which first appeared in a Russian paper in 1958 for a generalised Liénard system, a uniqueness theorem of limit cycles of a predator-prey system, which includes Lotka-Volterra, Gause and other systems as special cases, is obtained. Several examples show that the theorem is very useful in dealing with the uniqueness problem of limit cycles for certain ecological systems.

MSC:
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
92D25 Population dynamics (general)
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