Geodesic
Existence and global asymptotic stability of positive periodic solutions of a Lotka-Volterra type competition systems with delays and feedback controls
Electronic Journal of Differential Equations, Tome 2013 (2013).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The existence of positive periodic solutions of a periodic Lotka-Volterra type competition system with delays and feedback controls is studied by applying the continuation theorem of coincidence degree theory. By contracting a suitable Liapunov functional, a set of sufficient conditions for the global asymptotic stability of the positive periodic solution of the system is given. A counterexample is given to show that the result on the existence of positive periodic solution in [4] is incorrect.
Classification : 34K13, 92B05, 92D25, 93B52
Keywords: Lotka-Volterra competition system, time delay, feedback control, positive periodic solution, global asymptotic stability, continuation theorem 
@article{EJDE_2013__2013__a79,
     author = {Trinh, Anh Tuan},
     title = {Existence and global asymptotic stability of positive periodic solutions of a {Lotka-Volterra} type competition systems with delays and feedback controls},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2013},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a79/}
}
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Trinh, Anh Tuan. Existence and global asymptotic stability of positive periodic solutions of a Lotka-Volterra type competition systems with delays and feedback controls. Electronic Journal of Differential Equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a79/