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

Demou Luo; Qiru Wang

doi:10.3934/dcdsb.2020238

Article Contents

2021, Volume 26, Issue 6: 3427-3453. Doi: 10.3934/dcdsb.2020238

This issue Previous Article Global existence and Gevrey regularity to the Navier-Stokes-Nernst-Planck-Poisson system in critical Besov-Morrey spaces Next Article On 3d dipolar Bose-Einstein condensates involving quantum fluctuations and three-body interactions

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

Demou Luo and
Qiru Wang^,

School of Mathematics, Sun Yat-sen University, Guangzhou 510275, Guangdong, China

^* Corresponding author: mcswqr@mail.sysu.edu.cn
^* Corresponding author: mcswqr@mail.sysu.edu.cn

Received: April 30, 2020

Revised: May 31, 2020

Early access: August 2020

Published: June 2021

This research was supported by the National Natural Science Foundation of China (No. 11671406)

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Abstract

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.

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

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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} $

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

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

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