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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.
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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