带有经济效益的时滞分数阶微分-代数捕食-被捕食系统的Hopf分岔

Abstract

Abstract:

A fractional differential-algebraic biological economic system with harvest and time delay is firstly proposed and investigated in this paper. By using the Hopf bifurcation theory, some sufficient conditions for the existence of Hopf bifurcation induced by delay are obtained. The results show that in the case of zero economic profit, the biological equilibrium point of the system is asymptotically stable. Under positive economic profit condition, the system produces limit cycles at the positive equilibrium point as the delay increases through a certain threshold. It is found that fractional exponent, economic interest and delay can affect the other dynamic behavior of the system through some numerical simulations.

Key words: Fractional system, Hopf bifurcation, Time delay

CLC Number:

O175.1

Daoxiang Zhang,Ben Li,Dandan Chen,Yating Lin,Xinmei Wang. Hopf Bifurcation for a Fractional Differential-Algebraic Predator-Prey System with Time Delay and Economic Profit[J].Acta mathematica scientia,Series A, 2022, 42(2): 570-582.

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Figures/Tables 17

References 29

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变量(参数)	意义
$P\left( t \right)$	浮游植物的密度
$Z\left( t \right)$	浮游动物的密度
$a$	浮游植物种内干扰系数
$b$	成熟捕食者的捕食率
$c$	反应时间
$d$	捕食者(浮游动物)之间的干扰程度
$e$	喂食率
$g$	转换效率
$h$	浮游动物的死亡率
$\tau$	时滞
$f\left( {P, Z} \right) = \frac{{P}}{{1 + cP + dZ + ePZ}}$	Crowley-Martin^[13] 功能反应

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Hopf Bifurcation for a Fractional Differential-Algebraic Predator-Prey System with Time Delay and Economic Profit

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