A predator-prey model with generic birth and death rates for the predator and Beddington-DeAngelis functional response

Tihomir Ivanov*, Neli Dimitrova


Since the Lotka-Volterra model was published, a lot of work has been devoted to studying the interactions between predator and preypopulations. In 2014, A. J. Terry proposed a new model [1], which is a generalization of the well-known Rosenzweig-MacArthur model [2]. In his model Terry removes the hypothesis of a constant death rate anda linear (with respect to the functional response) growth rate for the predator,that underline the Rosenzweig-MacArthur model (and other classical models). This certainly makes the model more realistic. 
It should be mentioned, however, that a Holling Type-II functional response is used in the Terry's model.In [3] it is discussed that in many cases the Beddington-DeAngelis functional responce is to be preferred, since it gives a better fit to experimental data.Thus, we further modify the Terry's model by using theBeddington-DeAngelis functional response and study the behaviour of the solutions of the obtainedsystem.


[1] Terry, A. J.: A predator prey model with generic birthand death rates for the predator. Mathematical Biosciences 248 (2014), 57--66.

[2] Rosenzweig, M., MacArthur, R.: Graphical Representation and Stability Conditions ofPredator-Prey Interaction. American Naturalist (1963), 209--223.

[3] Skalski, G. T., Gilliam, J. F.: Functional Responses withPredator Interference: Viable Alternatives to the Holling Type II Model.Ecology 82(11) (2001), 3083--3092.

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DOI: http://dx.doi.org/10.11145/287


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