Utilize este identificador para referenciar este registo: http://hdl.handle.net/10400.21/2731
Título: Dynamical analysis in growth models: Blumberg’s equation
Autor: Leonel Rocha, José Leonel
Aleixo, Sandra Maria
Palavras-chave: Population dynamics
Blumberg's equation
Topological entropy
Kneading theory
Bifurcations and chaos
Symbolic dynamics
Beta(p, q) densities
Data: Mai-2013
Editora: Amer Inst Mathematical Sciences
Citação: Leonel Rocha, J. ; Aleixo, Sandra M. - Dynamical analysis in growth models: Blumberg’s equation. Discrete and Continuous dynamical systems - series B. ISSN 1531-3492. Vol. 18, nr 3 (2013), p. 783-795.
Resumo: We present a new dynamical approach to the Blumberg's equation, a family of unimodal maps. These maps are proportional to Beta(p, q) probability densities functions. Using the symmetry of the Beta(p, q) distribution and symbolic dynamics techniques, a new concept of mirror symmetry is defined for this family of maps. The kneading theory is used to analyze the effect of such symmetry in the presented models. The main result proves that two mirror symmetric unimodal maps have the same topological entropy. Different population dynamics regimes are identified, when the intrinsic growth rate is modified: extinctions, stabilities, bifurcations, chaos and Allee effect. To illustrate our results, we present a numerical analysis, where are demonstrated: monotonicity of the topological entropy with the variation of the intrinsic growth rate, existence of isentropic sets in the parameters space and mirror symmetry.
Peer review: yes
URI: http://hdl.handle.net/10400.21/2731
ISSN: 1531-3492
Aparece nas colecções:ISEL - Matemática - Artigos

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