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Stability analysis on a predator-prey system with distributed delays. (English) Zbl 0897.34062
A Lotka-Volterra predator-prey system with distributed delays is considered and local and global dynamical properties of two possible equilibria $P_1= (x_0,0)$ and $P_2= (x^*, y^*)$ are discussed. It is shown that when the delays are sufficiently small, if $P_2$ does not exist, then $P_1$ is globally asymptotically stable or globally attractive; otherwise, $P_2$ is locally asymptotically stable. Furthermore, a region of explicit asymptotic stability is obtained for $P_2$ based on a Lyapunov functional.

MSC:
34K20Stability theory of functional-differential equations
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References:
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