On global asymptotic stability of the equilibrium of “predator–prey” system in varying environment
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This paper considers a predator–prey system of differential equations. This ecological system is a model of Lotka–Volterra type whose prey population receives time-variation of the environment. It is not assumed that the time-varying coefficient is weakly integrally positive. We obtain sufficient conditions of global asymptotic stability of the unique interior equilibrium if the time-variation is bounded.
Keywordsglobal asymptotic stability Lotka–Volterra predator–prey model
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- 7.Vijaya, L. G. M., Vijaya, S., Gunasekaram, M. “Stability Analysis in Dynamics of Prey–Predator Model with Holling Type IV Functional Response and Intra-Specific Competition”, Research Inventy: International Journal of Engineering and Science 4, No. 1, 52–61 (2014).Google Scholar
- 10.Persidskii, K. P. “On Stability of Motion at First Approximation”, Matem. Sborn. 40, 284–293 (1933) [in Russian].Google Scholar
- 11.Lyapunov, A. M. Collected Works in Three Volumes (Akad. Nauk SSSR, Moscow–Leningrad, 1956), Vol. 2 [in Russian].Google Scholar