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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.

MSC:
34F05 Ordinary differential equations and systems with randomness
92D25 Population dynamics (general)
34D05 Asymptotic properties of solutions to ordinary differential equations
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[1] Arat√≥, M., A famous nonlinear stochastic equation (lotka – volterra model with diffusion), Math. comput. modelling, 38, 709-726, (2003) · Zbl 1049.92030
[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
[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
[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
[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
[7] Lian, B.; Hu, S., Stochastic delay gilpin – ayala competition models, Stoch. dyn., 6, 4, 561-576, (2006) · Zbl 1117.34079
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