Partial Survival and Extinction of Species in Discrete Nonautonomous Lotka-Volterra Systems
نویسندگان
چکیده
منابع مشابه
Partial Survival and Extinction of Species in Nonautonomous Lotka-Volterra Systems with Delays
This paper concerns with the principle of competitive exclusion which is extended by Shair Ahmad (1999, Proceedings of the American Mathematical Society 127, 29052910), that is, if the coefficients satisfy certain inequalities, then any solution with positive components at some point will have all of its last n − 1 components tend to zero, while the first one will stabilize at a certain solutio...
متن کاملExtinction of Species in Nonautonomous Lotka-volterra Systems
A nonautonomous nth order Lotka-Volterra system of differential equations is considered. It is shown that if the coefficients satisfy certain inequalities, then any solution with positive components at some point will have all of its last n − 1 components tend to zero, while the first one will stabilize at a certain solution of a logistic equation.
متن کاملExtinction in Nonautonomous Competitive Lotka-volterra Systems
It is well known that for the two species autonomous competitive Lotka-Volterra model with no fixed point in the open positive quadrant, one of the species is driven to extinction, whilst the other population stabilises at its own carrying capacity. In this paper we prove a generalisation of this result to nonautonomous systems of arbitrary finite dimension. That is, for the n species nonautono...
متن کاملPersistence and Extinction for General Nonautonomous n-Species Lotka–Volterra Cooperative Systems with Delays
The general nonautonomous n-species Lotka–Volterra cooperative systems with varying-time delays are studied. Sufficient conditions for the uniform strong persistence, uniform weak average persistence, uniform strong average persistence, and extinction of populations are obtained by applying the method of Liapunov functionals. Particularly, when the intrinsic growth rate of a species is nonposit...
متن کاملStatistics of extinction and survival in Lotka-Volterra systems
We analyze purely competitive many-species Lotka-Volterra systems with random interaction matrices, focusing the attention on statistical properties of their asymptotic states. Generic features of the evolution are outlined from a semiquantitative analysis of the phase-space structure, and extensive numerical simulations are performed to study the statistics of the extinctions. We find that the...
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ژورنال
عنوان ژورنال: Tokyo Journal of Mathematics
سال: 2005
ISSN: 0387-3870
DOI: 10.3836/tjm/1244208288