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Mokni, Karima; Elaydi, Saber; Ch-Chaoui, Mohamed; Eladdadi, Amina

Discrete evolutionary population models: a new approach. (English) Zbl 1442.92106

J. Biol. Dyn. 14, No. 1, 454-478 (2020).
Summary: In this paper, we apply a new approach to a special class of discrete time evolution models and establish a solid mathematical foundation to analyse them. We propose new single and multi-species evolutionary competition models using the evolutionary game theory that require a more advanced mathematical theory to handle effectively. A key feature of this new approach is to consider the discrete models as non-autonomous difference equations. Using the powerful tools and results developed in our recent work [Discrete Contin. Dyn. Syst., Ser. B 25, No. 3, 903–915 (2020; Zbl 1436.37023)], we embed the non-autonomous difference equations in an autonomous discrete dynamical systems in a higher dimension space, which is the product space of the phase space and the space of the functions defining the non-autonomous system. Our current approach applies to two scenarios. In the first scenario, we assume that the trait equations are decoupled from the equations of the populations. This requires specialized biological and ecological assumptions which we clearly state. In the second scenario, we do not assume decoupling, but rather we assume that the dynamics of the trait is known, such as approaching a positive stable equilibrium point which may apply to a much broader evolutionary dynamics.

Cited in 13 Documents

MSC:

92D15 Problems related to evolution
92D25 Population dynamics (general)
91A22 Evolutionary games
91A80 Applications of game theory

Keywords:

trait; evolutionary models; non-autonomous; stability; Darwinian; Beverton-Holt; Ricker; predator-prey

Citations:

Zbl 1436.37023
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References:

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