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A Lyapunov function for Leslie-Gower predator-prey models. (English) Zbl 0999.92036
Summary: A Lyapunov function for continuous-time Leslie-Gower predator-prey models [see P.H. Leslie, Biometrika 45, 16-31 (1958; Zbl 0089.15803); ibid. 35, 213-245 (1948; Zbl 0034.23303)] is introduced. Global stability of the unique coexisting equilibrium state is thereby established.

92D40 Ecology
34D23 Global stability of solutions to ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
92D25 Population dynamics (general)
Full Text: DOI
[1] Leslie, P.H., Some further notes on the use of matrices in population mathematics, Biometrika, 35, 213-245, (1948) · Zbl 0034.23303
[2] Leslie, P.H., A stochastic model for studying the properties of certain biological systems by numerical methods, Biometrika, 45, 16-31, (1958) · Zbl 0089.15803
[3] Pielou, E.C., Mathematical ecology, (1977), John Wiley & Sons New York · Zbl 0259.92001
[4] Barbashin, E.A., Introduction to the theory of stability, (1970), Wolters-Noordhoff Groningen · Zbl 0198.19703
[5] LaSalle, J.; Lefschetz, S., Stability by Liapunov’s direct method, (1961), Academic Press New York
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