Fractional dynamics of populations |
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Authors: | Margarita RiveroJuan J Trujillo Luis Vázquez |
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Institution: | a Departamento de Matemática Fundamental, Universidad de La Laguna, 38271 La Laguna, Tenerife, Spain b Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain c Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna, Tenerife, Spain |
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Abstract: | Nature often presents complex dynamics, which cannot be explained by means of ordinary models. In this paper, we establish an approach to certain fractional dynamic systems using only deterministic arguments. The behavior of the trajectories of fractional non-linear autonomous systems around the corresponding critical points in the phase space is studied. In this work we arrive to 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. |
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Keywords: | Fractional differential equations Dynamic systems Critical points Phase plane |
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