Global stability in n-species competition modelled by ``pure-delay-type'' systems -- II: nonautonomous case


K. Gopalsamy and Xue-zhong He


Research Report 96-15
Date: April 1996


Sufficient conditions are obtained for the global extreme stability of the positive solutions of a Lotka-Volterra type n-species nonautonomous competition system modelled by equations of the ``pure-delay-type''. Estimates of delays are derived for the persistence of stable systems. The existence and global stability of positive periodic and almost periodic solutions of the periodic and almost periodic systems are discussed. The method used is based on the construction of Lyapunov-type functionals for nonautonomous systems; the results obtained include and improve some of the existing results on nonatonomous competition systems both with and without delays.

Key phrases

n-species Lotka-Volterra nonautonomous system. competition. delays. periodic and almost periodic solutions. Lyapunov functionals. existence. global attractivity.

AMS Subject Classification (1991)

Primary: 34D05, 34C25, 34K20, 92A1


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