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Some new results of two-dimensional periodic Lotka-Volterra systems. (Chinese. English summary) Zbl 0913.34038

Summary: The author studies boundedness and persistence of solutions and existence and global stability of positive periodic solutions to two-dimensional periodic Lotka-Volterra predator-prey systems. He extends the obtained results to two-dimensional periodic Lotka-Volterra predator-prey systems with prey supplement and two-dimensional periodic Lotka-Volterra competition systems. A series of new criteria is obtained. The main results in [S. Ahmad, J. Math. Anal. Appl. 127, 377-387 (1987; Zbl 0648.34037), C. Alvarez, A. C. Lazer, J. Aust. Math. Soc., Ser. B 28, 202-219 (1986; Zbl 0625.92018)] are improved and extended.

MSC:

34C25 Periodic solutions to ordinary differential equations
92D25 Population dynamics (general)
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