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Necessary and sufficient conditions for existence of positive periodic solutions of periodic predator-prey systems. (Chinese. English summary) Zbl 0914.92019

Summary: The periodic Lotka-Volterra predator-prey systems are studied. Applying methods of bifurcation theory and differential inequality principle a necessary and sufficient criterion for existence of positive periodic solutions is established. Some main results of J. M. Cushing [see, e.g., SIAM J. Appl. Math. 32, 82-95 (1977; Zbl 0348.34031)], Z. Amine and R. Ortega [J. Math. Anal. Appl. 185, No. 2, 477-489 (1994; Zbl 0808.34043)] and Z. Ma and W. Wang [Appl. Anal. 34, No. 1, 79-90 (1989; Zbl 0658.34044)] are summarized and extended.

MSC:

92D25 Population dynamics (general)
34C25 Periodic solutions to ordinary differential equations
92D40 Ecology
34C23 Bifurcation theory for ordinary differential equations
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