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Dynamic analysis on an almost periodic predator-prey system with impulsive effects and time delays

This research was supported by the National Natural Science Foundation of China (No. 11671406)
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  • This article is concerned with a generalized almost periodic predator-prey model with impulsive effects and time delays. By utilizing comparison theorem and constructing a feasible Lyapunov functional, we obtain sufficient conditions to guarantee the permanence and global asymptotic stability of the system. By applying Arzelà-Ascoli theorem, we establish the existence and uniqueness of almost-periodic positive solutions. A feasible numerical simulation is provided to explain the suitability of our main criteria.

    Mathematics Subject Classification: Primary: 34K14, 34K20, 34K45; Secondary: 92D25.


    \begin{equation} \\ \end{equation}
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  • Figure 1.  Numeric simulation of the prey $ x(t) $ and the predator $ y(t) $ of (42) with the initial conditions $ (x(0),y(0))^{T} = (0.6,0.3)^{T} $, $ (x(0),y(0))^{T} = (0.2,0.1)^{T} $ and $ (x(0),y(0))^{T} = (0.4,0.2)^{T} $

    Table 1.  The biological parameters of $ x $ and $ y $

    $a_{i}^{l}$ $a_{i}^{u}$ $b_{i}^{l}$ $b_{i}^{u}$ $c_{i}^{l}$ $c_{i}^{u}$ $m_{i}^{l}$ $M_{i}^{u}$ $P_{i}^{l}$ $\tau_{i}^{l}$ $\tau_{i}^{u}$
    $x$ $0.25$ $0.35$ $0.94$ $0.96$ $0.11$ $0.11$ $0.2495$ $0.3736$ $0.01$ $0.01$ $0.01$
    $y$ $0.45$ $0.55$ $1.20$ $3.80$ $3.00$ $3.00$ $0.0189$ $0.5451$ $0.02$ $0.02$ $0.02$
     | Show Table
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