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Asymptotic behaviour of the stochastic Gilpin-Ayala competition models. (English) Zbl 1195.34083
Summary: We investigate a stochastic Gilpin-Ayala competition system, which is more general and more realistic than the classical Lotka-Volterra competition system. We discuss the asymptotic behaviour in detail of the stochastic Gilpin-Ayala competition system, and compare the classical Lotka-Volterra with Gilpin-Ayala competition system.

34F05ODE with randomness
92D25Population dynamics (general)
34D05Asymptotic stability of ODE
Full Text: DOI
[1] Arat√≥, M.: A famous nonlinear stochastic equation (Lotka -- Volterra model with diffusion), Math. comput. Modelling 38, 709-726 (2003) · Zbl 1049.92030 · doi:10.1016/S0895-7177(03)90056-2
[2] Mao, X.; Marion, G.; Renshaw, E.: Environmental Brownian noise suppresses explosions in populations dynamics, Stochastic process. Appl. 97, 95-110 (2002) · Zbl 1058.60046 · doi:10.1016/S0304-4149(01)00126-0
[3] Mao, X.; Sabanis, S.; Renshaw, E.: Asymptotic behaviour of the stochastic Lotka -- Volterra model, J. math. Anal. appl. 287, 141-156 (2003) · Zbl 1048.92027 · doi:10.1016/S0022-247X(03)00539-0
[4] Takeuchi, Y.: Diffusion effect on stability of Lotka -- Volterra models, Bull. math. Biol. 48, 585-601 (1986) · Zbl 0613.92025
[5] Fan, M.; Wang, K.: Global periodic solutions of a generalized n-species gilpin -- ayala competition model, Comput. math. Appl. 40, 1141-1151 (2000) · Zbl 0954.92027 · doi:10.1016/S0898-1221(00)00228-5
[6] Gilpin, M. E.; Ayala, F. J.: Global models of growth and competition, Proc. natl. Acad. sci. USA 70, 3590-3593 (1973) · Zbl 0272.92016 · doi:10.1073/pnas.70.12.3590
[7] Lian, B.; Hu, S.: Stochastic delay gilpin -- ayala competition models, Stoch. dyn. 6, No. 4, 561-576 (2006) · Zbl 1117.34079 · doi:10.1142/S0219493706001888