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metadata.artigo.dc.title: Data collapse, scaling functions, and analytical solutions of generalized growth models
metadata.artigo.dc.creator: Cabella, Brenno Caetano Troca
Martinez, Alexandre Souto
Ribeiro, Fabiano
metadata.artigo.dc.subject: Population dynamics model
Data collapse
Scaling functions
Analytical solutions
Modelo de dinâmica populacional
Colapso de dados
Funções de escala
Soluções analíticas
metadata.artigo.dc.publisher: American Physical Society 2011
metadata.artigo.dc.identifier.citation: CABELLA, B. C. T.; MARTINEZ, A. S.; RIBEIRO, F. Data collapse, scaling functions, and analytical solutions of generalized growth models. Physical Review E, Melville, v. 83, 061902, p. 1-7, 2011. doi:
metadata.artigo.dc.description.abstract: We consider a nontrivial one-species population dynamics model with finite and infinite carrying capacities. Time-dependent intrinsic and extrinsic growth rates are considered in these models. Through the model per capita growth rate we obtain a heuristic general procedure to generate scaling functions to collapse data into a simple linear behavior even if an extrinsic growth rate is included. With this data collapse, all the models studied become independent from the parameters and initial condition. Analytical solutions are found when time-dependent coefficients are considered. These solutions allow us to perceive nontrivial transitions between species extinction and survival and to calculate the transition’s critical exponents. Considering an extrinsic growth rate as a cancer treatment, we show that the relevant quantity depends not only on the intensity of the treatment, but also on when the cancerous cell growth is maximum.
metadata.artigo.dc.language: en_US
Appears in Collections:DFI - Artigos publicados em periódicos

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