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In this Note, we describe the stationary equilibria and the asymptoticbehaviour of an heterogeneous logistic reaction-diffusion equation under theinfluence of autonomous or time-periodic forcing terms. We show that the studyof the asymptotic behaviour in the time-periodic forcing case can be reduced tothe autonomous one, the last one being described in function of the "size" ofthe external perturbation. Our results can be interpreted in terms of maximalsustainable yields from populations. We briefly discuss this last aspectthrough a numerical computation.

Models of population dynamics under the influence of external perturbations: mathematical results