2005 Fiscal Year Final Research Report Summary
Accuracy and atability for delayed integral and differential equations and their discrete equations
| Project/Area Number |
16540207
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Waseda University |
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Principal Investigator |
MUROYA Yoshiaki Waseda University, Faculty of Science and Engineering, Professor, 理工学術院, 教授 (90063718)
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| Project Period (FY) |
2004 – 2005
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| Keywords | global asymptotic stability / Lotka-Volterra system / stability of discrete model / permanence / persistence |
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| Research Abstract |
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
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