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Persistence and extinction of a stochastic delay predator-prey model under regime switching

Zhen Hai Liu, Qun Liu (2014)

Applications of Mathematics

The paper is concerned with a stochastic delay predator-prey model under regime switching. Sufficient conditions for extinction and non-persistence in the mean of the system are established. The threshold between persistence and extinction is also obtained for each population. Some numerical simulations are introduced to support our main results.

Positive periodic solution for ratio-dependent n -species discrete time system

Mei-Lan Tang, Xin-Ge Liu (2011)

Applications of Mathematics

In this paper, sharp a priori estimate of the periodic solutions is obtained for the discrete analogue of the continuous time ratio-dependent predator-prey system, which is governed by nonautonomous difference equations, modelling the dynamics of the n - 1 competing preys and one predator having nonoverlapping generations. Based on more precise a priori estimate and the continuation theorem of the coincidence degree, an easily verifiable sufficient criterion of the existence of positive periodic solutions...

Positive periodic solutions of N -species neutral delay systems

Hui Fang (2003)

Czechoslovak Mathematical Journal

In this paper, we employ some new techniques to study the existence of positive periodic solution of n -species neutral delay system N i ' ( t ) = N i ( t ) a i ( t ) - j = 1 n β i j ( t ) N j ( t ) - j = 1 n b i j ( t ) N j ( t - τ i j ( t ) ) - j = 1 n c i j ( t ) N j ' ( t - τ i j ( t ) ) . As a corollary, we answer an open problem proposed by Y. Kuang.

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