Permanence and stability in multi-species non-autonomous Lotka-Volterra competitive systems with delays and feedback controls

Authors:
Linfei Nie;Jigen Peng;Zhidong Teng
Affiliations:
Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049, China and College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China;Institute for Information and System Sciences, Research Center for Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049, China;College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2009

Citing 4
Cited 1

Periodic solutions of single-species models with periodic delay

SIAM Journal on Mathematical Analysis
On a property of nonautonomous Lotka-Volterra competition model

Nonlinear Analysis: Theory, Methods & Applications
Existence and global attractivity of positive periodic solutions of functional differential equations with feedback control

Journal of Computational and Applied Mathematics
Permanence and periodic solution in competitive system with feedback controls

Mathematical and Computer Modelling: An International Journal

Permanence and stability in non-autonomous predator-prey Lotka-Volterra systems with feedback controls

Computers & Mathematics with Applications

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Abstract

In this paper, we consider a multi-species Lotka-Volterra type competitive system with delays and feedback controls. A general criteria on the permanence is established, which is described by integral form and independent of feedback controls. By constructing suitable Lyapunov functionals, a set of easily verifiable sufficient conditions are derived for global stability of any positive solution to the model.