| THE EXISTENCE AND STABILITY OF THE HETEROCLINIC CYCLE IN A KIND OF BIOLOGICAL SYSTEM |
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| 作者姓名： | 杨翠红 梁肇军 |
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| 作者单位： | Yang Cuihong(Dept. of Math.，Zhongshan University，Guangrkou 510275)Liang Zhaojun(Dept. of Math.，Central China Normal University，Wuhan 430079) |
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| 基金项目： | This research is supported by NNSF of China． |
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| 摘 要： | IIntroductlonConsider the n－spedes biological systemlit\1．＝IJ!厂．＋》*i,工上D、忍＝上,’··。n．ti)Ifffi＝1,it is S S－SpSCllS LOthaka－VoltOOYY SystSS．Iftti＝2,It Is S S－sPeCieSKolmongorov system．As to the n－spedes Gause－Lotb－Volterra system矿ti 乙工．＝T;Ii、y Qiil．I。Ti 7 U,on M U,t6)174 AnnofDiff Eqs．VO18M叫 and Leonard1],Ho凡aner and Sigmund问 have studied this system forthe case n二 3 respectlvelyand noted that thereprobably exists aheterocllnlccyclefor…
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THE EXISTENCE AND STABILITY OF THEHETEROCLINIC CYCLE IN A KIND OFBIOLOGICAL SYSTEM |
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| Yang Cuihong.THE EXISTENCE AND STABILITY OF THE HETEROCLINIC CYCLE IN A KIND OF BIOLOGICAL SYSTEM[J].微分方程年刊(英文版),2002(2). |
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| Authors: | Yang Cuihong |
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| Abstract: | In this paper, we study the n-species biological systemwe get sufficient conditions for the existence of the invariant plane to system (1) whenm=1 and m = 2, we also get sufficient conditions for the eristence and stability ofthe heteroclinic cycle to system (1) when m = 1 and m = 2. In the case m = 1 andn = 3, we get conditions for the existence and stability of the heteroclinic cycle on theinvariant plane of system (1). In this case, we also prove that there is a center insidethe heteroclinic cycle and bounded by this heteroclinic cycle. |
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| Keywords: | invariant plane heteroclinic cycle existence stability n-species Lotka-Volterra system n-species Kolmongorov system |
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