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The influence of the type 3 sigmoid functional response upon the stability of predator prey difference models



The influence of the type 3 sigmoid functional response upon the stability of predator prey difference models



Theoretical Population Biology 18(2): 257-278



Sigmoid functional responses exert a stabilizing influence upon a discrete-generation predator-prey model in a way analogous to that found in continuous predator-prey models. The precise effect depends upon the degree to which a predator's feeding history influences its reproductive success. The time delay intrinsic in difference equation models imposes constraints not found in differential models; in an otherwise unstable model the inclusion of a sigmoid function response can result in local stability. With the addition of prey self-regulation the stabilizing influence of the functional response acts in concert with self-regulation, as it does in continuous models. The effect of the sigmoid response upon stability is not dependent upon the assumption of continuity; sigmoid responses could be an important factor stabilizing natural communities.

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Accession: 006701620

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