一类具有非线性扩散和时滞的捕食系统的持续性与周期解

徐国明;贾建文

系统科学与数学 ›› 2010, Vol. 30 ›› Issue (4) : 515-529.

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中国科学院数学与系统科学研究院期刊网
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系统科学与数学 ›› 2010, Vol. 30 ›› Issue (4) : 515-529. DOI: 10.12341/jssms08968
论文

一类具有非线性扩散和时滞的捕食系统的持续性与周期解

    徐国明(1); 贾建文(2)
作者信息 +

Persistence and Periodic Solution of a Predator-Prey System with Nonlinear Diffusion and Delay

    XU Guoming(1); JIA Jianwen(2)
Author information +
文章历史 +

摘要

研究了一类具有非线性扩散和Beddington--Deangelis功能性反应,且同时具有连续时滞和离散
时滞的非自治两食饵一捕食者系统,证明了在适当条件下该系统是一致持久的,并且得到了系统正周期解全局渐近稳定的充分条件.最后,给出一个例子以说明得到的结果.

Abstract

This paper considers a kind of nonautonomous Two-prey One-predator models with nonlinear diffusion, Beddington-Deangelis functional response, discrete delay and continuous time delay. It is proved that the system can be persistent under certain conditions. Furthermore, sufficient conditions which guarantee the global asymptotic stability of positive periodic solution of the system are obtained. Finally, an example is given to demonstrate the results.

关键词

非线性扩散 / 时滞 / 一致持久 / 正周期解.

Key words

Nonlinear diffusion / delay / uniform persistence / positive periodic solution.

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徐国明 , 贾建文. 一类具有非线性扩散和时滞的捕食系统的持续性与周期解. 系统科学与数学, 2010, 30(4): 515-529. https://doi.org/10.12341/jssms08968
XU Guoming , JIA Jianwen. Persistence and Periodic Solution of a Predator-Prey System with Nonlinear Diffusion and Delay. Journal of Systems Science and Mathematical Sciences, 2010, 30(4): 515-529 https://doi.org/10.12341/jssms08968
中图分类号： 34C25    34D05    92D25   
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