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Li, Zhong; Chen, Fengde

Extinction in two dimensional nonautonomous Lotka-Volterra systems with the effect of toxic substances. (English) Zbl 1113.92065

Appl. Math. Comput. 182, No. 1, 684-690 (2006).
Summary: We consider a nonautonomous competitive Lotka-Volterra system of two species with the effect of toxic substances. It is shown that toxic substances play an important role in the extinction of species. We prove that one of the components will be driven to extinction while the other will stabilize at a certain solution of a logistic equation under some conditions.

Cited in 3 Reviews
Cited in 31 Documents

MSC:

92D40 Ecology
34C60 Qualitative investigation and simulation of ordinary differential equation models
37N25 Dynamical systems in biology

Keywords:

extinction; nonautonomous; toxicology; competition
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\textit{Z. Li} and \textit{F. Chen}, Appl. Math. Comput. 182, No. 1, 684--690 (2006; Zbl 1113.92065)
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References:

[1] Ahmad, S., On the nonautonomous volterra – lotka competition equations, Proceedings of the American mathematical society, 117, 199-204, (1993) · Zbl 0848.34033
[2] Ahmad, S.; Lazer, A.C., On a property of nonautonomous lotka – volterra competition model, Nonlinear analysis, 37, 603-611, (1999) · Zbl 0930.34038
[3] Francisco Montes De Oca, Miguel Vivas, Extinction in two dimensional Lotka-Volterra system with infinite delay, Nonlinear Analysis, Real World Application, in press. · Zbl 1122.34058
[4] Chattopadhyay, J., Effect of toxic substances on a two-species competitive system, Ecological modelling, 84, 287-289, (1996)
[5] Montes De Oca, Francisco; Zeeman, M.L., Extinction in nonautonomous competitive lotka – volterra systems, Proceedings of the American mathematical society, 124, 12, 3677-3687, (1996) · Zbl 0866.34029
[6] Chen, F.D.; Shi, J.L., Periodicity in a logistic type system with several delays, Computer and mathematics with applications, 48, 1-2, 35-44, (2004) · Zbl 1061.34050
[7] Mahhuba, R., On the nonautonomous lotka – volterra competition system with diffusion, Journal of xinjiang university, 13, 3, 13-16, (1996), (in Chinese) · Zbl 0964.92511
[8] Chen, F.D., Positive periodic solutions of neutral lotka – volterra system with feedback control, Applied mathematics and computation, 162, 3, 1279-1302, (2005) · Zbl 1125.93031
[9] Chen, F.D., On a nonlinear non-autonomous predator – prey model with diffusion and distributed delay, Journal of computational and applied mathematics, 180, 1, 33-49, (2005) · Zbl 1061.92058
[10] Tineo, A., Asymptotic behaviour of positive solutions of the nonautonomous lotka – volterra competition equations, Differential and integral equations, 6, 419-457, (1993) · Zbl 0774.34037
[11] Hirsch, W.; Hanisch, H.; Gabriel, J., Differential equation models of some parasitic infection-methods for the study of asymptotic behavior, Communication on pure applied mathematics, 38, 733-753, (1985) · Zbl 0637.92008
[12] Chen, F.D., Persistence and periodic orbits for two-species non-autonomous diffusion lotka – voltrra models, Applied mathematics journal of Chinese university series B, 19, 4, 359-366, (2004) · Zbl 1074.34053
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