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Stability analysis on a predator-prey system with distributed delays

✍ Scribed by Wanbiao Ma; Yasuhiro Takeuchi

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
625 KB
Volume
88
Category
Article
ISSN
0377-0427

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✦ Synopsis

This paper concerns the local and global dynamical properties of the nonnegative and positive equilibria of a Lotka-Volterra predator-prey system with distributed delays. It is shown that, while the positive equilibrium does not exist, the nonnegative equilibrium is globally asymptotically stable or globally attractive as long as the delays are small enough. If the positive equilibrium exists, it is shown that it is locally asymptotically stable when the delays are suitably small. Furthermore, an explicit asymptotic stability region for the positive equilibrium is also obtained based on a Liapunov functional.

πŸ“œ SIMILAR VOLUMES

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By using a fixed point theorem and Lyapunov functional, an especially easily checked criterion is obtained for the global existence and global asymptotic stability of positive periodic solutions of a periodic predator-prey system with infinite delays. Moreover, the global existence theorem is also s

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In this paper, a three-species predator-prey system with two delays is investigated. By choosing the sum s of two delays as a bifurcation parameter, we first show that Hopf bifurcation at the positive equilibrium of the system can occur as s crosses some critical values. Second, we obtain the formu