具有时滞的周期Lotka-Volterra型系统的全局渐近稳定性

Abstract

Abstract:

In this paper a general n-species periodic Lotka-Volterra type system with distributed delay and time dependent delay is considered. Sufficient conditions for the existence and global asymptotic stability of positive periodic solutions is established by applying the method of Liapunov functions. These conditions improve and extend the recent ones obtained by Wang, Chen and Lu ［2］and Ahlip and King［4］.

Key words: Ｌｏｔｋａ-Ｖｏｌｔｅｒｒａｓｙｓｔｅｍ, Ｄｅｌａｙ, Ｐｏｓｉｔｉｖｅｐｅｒｉｏｄｉｃｓｏｌｕｔｉｏｎ, Ｇｌｏｂａｌｓｔａｂｉｌｉｔｙ, Ｌｙａｐｕｎｏｖｆｕｎｃｔｉｏｎ

CLC Number:

３４Ｋ２０，９２Ｄ２５

Teng Zhidong Chen Lansun. Global Asymptotic Stability of Periodic Lotka-Volterra Systems with Delays[J].Acta mathematica scientia,Series A, 2000, 20(3): 296-303.

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References

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８　ＢｅｒｅｋｅｔｏｇｌｕＨ，ＧｏｙｒｉＩ．ＧｌｏｂａｌａｓｙｍｐｔｏｔｉｃａｌｓｔａｂｉｌｉｔｙｉｎａｎｏｎａｕｔｏｎｏｍｏｕｓＬｏｔｋａＶｏｌｔｅｒｒａｔｙｐｅｓｙｓｔｅｍｗｉｔｈｉｎｆｉｎｉｔｅｄｅｌａｙ．ＪＭａｔｈＡｎａｌＡｐｐｌ，１９９７，２１０（１）：２７９－２９１
９　ＦｒｅｅｄｍａｎＨＩ，ＲｕａｎＳ．Ｕｎｉｆｏｒｍｐｅｒｓｉｓｔｅｎｃｅｉｎｆｕｎｃｔｉｏｎａｌｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ．ＪＤｉｆｆｅｒｅｎｔｉａｌＥｑｕａｔｉｏｎｓ，１９９５，１１５（１）：１７５－１９２
１０　ＴａｎｇＢ，ＫｕａｎｇＹ．Ｐｅｒｍａｎｅｎｃｅｉｎｋｏｌｍｏｇｏｒｏｖｔｙｐｅｓｙｓｔｅｍｓｏｆｎｏｎａｕｔｏｎｏｍｏｕｓｆｕｎｃｔｉｏｎａｌｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ．ＪＭａｔｈＡｎａｌＡｐｐｌ，１９９６，１９７（２）：４２７－４４７
１１　李森林，温立志．泛函微分方程．湖南长沙：湖南科学技术出版社，１９８７，１２０－１８８
１２　ＥｉｌｂｅｃｋＪＣ，ＬｏｐｅｚＧｏｍｅｚＪ．ＯｎｔｈｅｐｅｒｉｏｄｉｃＬｏｔｋａＶｏｌｔｅｒｒａｃｏｍｐｅｔｉｔｉｏｎｍｏｄｅｌ．ＪＭａｔｈＡｎａｌＡｐｐｌ，１９９７，２１０（１）：５８－８７
１３　ＴｉｎｅｏＡ．Ａｎｉｔｅｒａｔｉｖｅｓｃｈｅｍｅｆｏｒｔｈｅｃｏｍｐｅｔｉｎｇｓｐｅｃｉｅｓｐｒｏｂｌｅｍ．ＪＤｉｆｆｅｒｅｎｔｉａｌＥｑｕａｔｉｏｎｓ，１９９５，１１６（１）：１－１５

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Global Asymptotic Stability of Periodic Lotka-Volterra Systems with Delays

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