Permanence and global stability in a Lotka-Volterra predator-prey system with delays Original Research Article

Consider the permanence and global asymptotic stability of models governed by the following Lotka-Volterra-type system: View the MathML source , with initial conditions View the MathML source . 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.