Dynamical behaviors determined by the Lyapunov function in competitive Lotka-Volterra systems
نویسندگان
چکیده
منابع مشابه
Dynamical behaviors determined by the Lyapunov function in competitive Lotka-Volterra systems.
Dynamical behaviors of the competitive Lotka-Volterra system even for 3 species are not fully understood. In this paper, we study this problem from the perspective of the Lyapunov function. We construct explicitly the Lyapunov function using three examples of the competitive Lotka-Volterra system for the whole state space: (1) the general 2-species case, (2) a 3-species model, and (3) the model...
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Global dynamical behaviors of the competitive Lotka-Volterra system even in 3-dimension are not fully understood. The Lyapunov function can provide us such knowledge once it is constructed. In this paper, we construct explicitly the Lyapunov function in three examples of the competitive LotkaVolterra system for the whole state space: (1) the general 2-dimensional case; (2) a 3-dimensional model...
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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 arbitrary finite dimension. That is, for the «-species autonomous competitive Lotka-Volte...
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For autonomous Lotka-Volterra systems of differential equations modelling the dynamics of n competing species, new criteria are established for the existence of a single point global attractor. Under the conditions of these criteria, some of the species will survive and stabilise at a steady state whereas the others, if any, will die out.
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ژورنال
عنوان ژورنال: Physical Review E
سال: 2013
ISSN: 1539-3755,1550-2376
DOI: 10.1103/physreve.87.012708