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Accuracy and atability for delayed integral and differential equations and their discrete equations

时滞积分微分方程及其离散方程的准确度和稳定性

基本信息

批准号：
16540207
负责人：
MUROYA Yoshiaki
金额：
$ 0.96万
依托单位：
Waseda University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2005
项目状态：
已结题

项目摘要

We have established the following results by this project :Conditions of permanence for the discrete models of nonautonomous Lotka-Volterra systems. ([21]).Conditions of persistence and global asymptotic stability for the discrete models of pure-delay Lotka-Volterra systems ([19], [20]).Another kind Condition of global asymptotic stability which is derived by using the main term of the equation ([16], [18]).Condition of global stability for the Lotka-Volterra system which has the dimension $n geq 2$ and at most one delay for each species. This condition improves the well-known stability conditions which were derived by K. Gopalsamy ([17]).Conditions of boundedness and partial survival for solutions for nonautonomous May-Leonard equation which were extended to nonautonomous delayed Lotka-Volterra systems ([15]).Conditions of contractivity and global asymptotic stability for general delayed logistic equations ([14]).A rigorous proof of a part of conjecture for global asymptotic stability … More of logistic equation which has one negative feedback term of piecewise constant delay and a friction term ([13]).Conditions of partial survival and extinction of species for discrete models of Lotka-Volterra type which were extended the results on the "principle of extinction" obtained by S. Ahmad ([12]).Conditions of global asymptotic stability for the zero solution of separable nonlinear delayed differential equations ([11]).Two sufficient conditions of contractivity for solutions of the discrete models of nonautonomous Lotka-Volterra type. We also show that the condition of global asymptotic stability obtained by W. Wang et al. satisfies the contractivity condition for autonomous case ([10]).Conditions of persistence and global asymptotic stability for solutions of pure-delay type nonautonomous Lotka-Volterra systems ([9]).A sufficient condition of permanence for system which is derived by applying both results proposed by S. Ahmad and A. C. Lazer and the partial survival for nonautonomous May-Leonald equations obtained by R. Redfeffer ([8]).Moreover, we obtain more results on the conditions of global asymptotic stability for differential equations and discrete equations ([1]-[7]). Less

通过本项目，我们建立了以下结果：非自治Lotka-Volterra系统离散模型的持续生存条件。（[21]）.纯时滞Lotka-Volterra系统离散模型的持久性和全局渐近稳定性条件（[19]，[20]）.利用方程的主项导出了另一类全局渐近稳定的条件（[16]，[18]）.维数为ngeq ~ 2且每个种群至多有一个时滞的Lotka-Volterra系统的全局稳定性条件.这个条件改进了K. Gopalsamy（[17]）.推广到非自治时滞Lotka-Volterra系统的非自治May-Leonard方程解的有界性和部分生存性条件（[15]）.一般时滞Logistic方程的压缩性和全局渐近稳定性条件（[14]）.关于全局渐近稳定性的一部分猜想的严格证明 ...更多信息本文讨论了具有分段常数时滞负反馈项和摩擦项的Logistic方程（[13]）的种群部分生存和灭绝的条件，推广了S. Ahmad（[12]）.可分非线性时滞微分方程零解的全局渐近稳定性条件（[11]）.非自治Lotka-Volterra型离散模型解的压缩性的两个充分条件.我们还证明了W. Wang等在文献[10]中给出了非自治Lotka-Volterra系统解的持续生存和全局渐近稳定的条件，在文献[9]中给出了非自治Lotka-Volterra系统解的持续生存和全局渐近稳定的条件，并应用S. Ahmad和A. C. Lazer和R. Redfeffer（[8]）的结果，进一步得到了微分方程和离散方程全局渐近稳定性条件的更多结果（[1]-[7]）。少