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On the periodic Lotka-Volterra competition model. (English) Zbl 0874.34039

Summary: We analyze the existence, stability and multiplicity of \(T\)-periodic coexistence states for the classical nonautonomous periodic Lotka-Volterra competing species model. This is done by treating the average values of the birth rates of species as parameters, and studying the global structure of the set of coexistence states as these parameters vary. As a result of this analysis, we can explain the interesting differences between the results for the periodic case and the associated autonomous model.

MSC:

34C25 Periodic solutions to ordinary differential equations
92D25 Population dynamics (general)
34C23 Bifurcation theory for ordinary differential equations
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