Permanence and global stability in a Lotka-Volterra predator-prey system with delays |
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Authors: | Y. Muroya |
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Affiliation: | Department of Mathematical Sciences, Waseda University 3-4-1 Ohkubo Shinjuku-ku, Tokyo, 169-8555, Japan |
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Abstract: | Consider the permanence and global asymptotic stability of models governed by the following Lotka-Volterra-type system: , with initial conditions xi(t) = φi(t) ≥ o, t ≤ t0, and φi(t0) > 0. 1 ≤ i ≤n . We define x0(t) = xn+1(t)≡0 and suppose that φi(t), 1 ≤ i ≤ n, are bounded continuous functions on [t0, + ∞) and γi, αi, ci > 0,γi,j ≥ 0, for all relevant i,j.Extending a technique of Saito, Hara and Ma[1] for n = 2 to the above system for n ≥ 2, we offer sufficient conditions for permanence and global asymptotic stability of the solutions which improve the well-known result of Gopalsamy. |
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Keywords: | Permanence Global asymptotic stability Lotkar-Volterra predator-prey system |
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