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Periodicity and stability for a Lotka-Volterra type competition system with feedback controls and deviating arguments. (English) Zbl 1216.34086
Summary: This paper deals with general periodic Lotka-Volterra type competition systems with feedback controls and deviating arguments. By employing fixed point index theory on a cone, an explicit necessary and sufficient condition for the global existence of a positive periodic solution is proved. By constructing a suitable Lyapunov functional, a set of easily verifiable sufficient conditions for the global asymptotic stability of the positive periodic solution is given.
MSC:
34K60Qualitative investigation and simulation of models
34K13Periodic solutions of functional differential equations
34K20Stability theory of functional-differential equations
92D25Population dynamics (general)
34K35Functional-differential equations connected with control problems
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