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)
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},
     year = {2013},
     volume = {2013},
     zbl = {1293.34108},
     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/