Fractional dynamics of populations. (English) Zbl 1226.92060

Summary: Nature often presents complex dynamics, which cannot be explained by means of ordinary models. We establish an approach to certain fractional dynamic systems using only deterministic arguments. The behavior of the trajectories of fractional nonlinear autonomous systems around the corresponding critical points in the phase space is studied. We arrive at several interesting conclusions; for example, we conclude that the order of fractional derivation is an excellent controller of the velocity how the mentioned trajectories approach to (or away from) the critical point. Such property could contribute to faithfully represent the anomalous reality of the competition among some species (in cellular populations as cancer or HIV). We use classical models, which describe dynamics of certain populations in competition, to give a justification of the possible interest of the corresponding fractional models in biological areas of research.


92D25 Population dynamics (general)
37N25 Dynamical systems in biology
34A08 Fractional ordinary differential equations
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