Generalized exponential function and discrete growth models

Alexandre Souto Martinez, Rodrigo Silva González and Aquino Lauri Espíndola

Physica A: Statistical Mechanics and its Applications, 2009, vol. 388, issue 14, 2922-2930

Abstract: Here we show that a particular one-parameter generalization of the exponential function is suitable to unify most of the popular one-species discrete population dynamic models into a simple formula. A physical interpretation is given to this new introduced parameter in the context of the continuous Richards model, which remains valid for the discrete case. From the discretization of the continuous Richards’ model (generalization of the Gompertz and Verhulst models), one obtains a generalized logistic map and we briefly study its properties. Notice, however that the physical interpretation for the introduced parameter persists valid for the discrete case. Next, we generalize the (scramble competition) θ-Ricker discrete model and analytically calculate the fixed points as well as their stabilities. In contrast to previous generalizations, from the generalized θ-Ricker model one is able to retrieve either scramble or contest models.

Keywords: Complex systems; Population dynamics (ecology); Nonlinear dynamics (search for similar items in EconPapers)
Date: 2009
References: View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:388:y:2009:i:14:p:2922-2930

DOI: 10.1016/j.physa.2009.03.035

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