## Abstract 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
Global Attractivity of the Periodic Lotka–Volterra System
✍ Scribed by Yang Pinghua; Xu Rui
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 86 KB
- Volume
- 233
- Category
- Article
- ISSN
- 0022-247X
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✦ Synopsis
A Lotka᎐Volterra periodic model with m-predators and n-preys is studied in this paper. A set of easily verifiable sufficient conditions that guarantee the existence, uniqueness and global attractivity of the positive periodic solutions is obtained. Finally, a suitable example is given to illustrate that the conditions of the main theorem are feasible.
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By using the continuation theorem of coincidence degree theory, sufficient and realistic conditions are obtained for the existence of positive periodic solutions for both periodic Lotka᎐Volterra equations and systems with distributed or statedependent delays. Our results substantially extend and imp
We analyze the existence, stability, and multiplicity of T-periodic coexistence states for the classical nonautonomous periodic Lotka᎐Volterra competing species model. This is done by treating the average values of the birth rates of species as parameters, and studying the global structure of the se