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Relaxation oscillation profile of limit cycle in predator-prey system. (English) Zbl 1176.34049

It is known that for a class of conventional predator-prey systems a stable limit cycle exists for a range of parameters. The aim of the paper is to study the asymptotic behavior of the unique limit cycle when the death rate of predator tends to zero. The author shows that the limit cycle behaves similar to a nonlinear relaxation oscillation.

MSC:

34C26 Relaxation oscillations for ordinary differential equations
34E15 Singular perturbations for ordinary differential equations
92D25 Population dynamics (general)
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