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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.

MSC:
92D40 Ecology
34D23 Global stability of solutions to ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
92D25 Population dynamics (general)
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[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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