Determine dynamical behaviors by the Lyapunov function in competitive Lotka-Volterra systems
Populations and Evolution
2014-03-26 v1 Classical Analysis and ODEs
Dynamical Systems
Exactly Solvable and Integrable Systems
Abstract
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 Lotka-Volterra system for the whole state space: (1) the general 2-dimensional case; (2) a 3-dimensional model; (3) the model of May-Leonard. The dynamics of these examples include bistable case and cyclical behavior. The first two examples are the generalized gradient system defined in the Appendixes, while the model of May-Leonard is not. Our method is helpful to understand the limit cycle problems in general 3-dimensional case.
Keywords
Cite
@article{arxiv.1210.7662,
title = {Determine dynamical behaviors by the Lyapunov function in competitive Lotka-Volterra systems},
author = {Ying Tang and Ruoshi Yuan and Yian Ma},
journal= {arXiv preprint arXiv:1210.7662},
year = {2014}
}
Comments
9 pages, 2 figures