Compensatory versus Overcompensatory Dynamics in Density-dependent Leslie Models

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The role of compensatory and overcompensatory dynamics in generating multiple attractors in density-dependent Leslie models with or without the Allee effects are studied. In the presence of the Allee effect the models support multiple attractors. However, in the absence of the Allee effect single attractors are supported when the dynamics are compensatory while multiple attractors are supported under overcompensatory dynamics. The existence of multiple attractors in density-dependent Leslie models implies that the qualitative population dynamics depend on initial conditions.