The criteria of ultimate boundedness for nonautonomous Lotka-Volterra tree systems |
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| Institution: | Institute of Systems Science, Academia Sinica Beijing 100080, P.R. China;Department of Mathematics, Xinyang Teachers College Henan 464000, P.R. China;Institute of Systems Science, Academia Sinica Beijing 100080, P.R. China;Department of Mathematics, Xinjiang University Urumqi 830046, P.R. China;Institute of Mathematics, Academia Sinica Beijing 100080, P.R. China |
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| Abstract: | In this paper, by introducing a concept called the degree of species, we obtain a set of sufficient conditions for the ultimate boundedness of nonautonomous n-species Lotka-Volterra tree systems. As a consequence, we also obtain the criteria of the existence of a globally stable equilibrium point for the autonomous Lotka-Volterra tree system. The criteria in this paper are in explicit forms of the parameters, and thus, are easily verifiable. |
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