Comportamento caótico em modelos matemáticos de câncer

Detalhes bibliográficos
Ano de defesa: 2014
Autor(a) principal: Silva, Patrícia Demétria Branco [UNESP]
Orientador(a): Não Informado pela instituição
Banca de defesa: Não Informado pela instituição
Tipo de documento: Dissertação
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: Universidade Estadual Paulista (Unesp)
Programa de Pós-Graduação: Não Informado pela instituição
Departamento: Não Informado pela instituição
País: Não Informado pela instituição
Palavras-chave em Português:
Link de acesso: http://hdl.handle.net/11449/113832
Resumo: In this work we study a system of ordinary differential equations which represent a mathematical model of cancer which has chaotic dynamics. In the study we use the bifurcation theory, especially the Hopf bifurcation and the period doubling bifurcation (flip), we also use the basic notion of symbolic dynamics. The model is analyzed from two points of view. In the first one we consider all the parameters as being fixed and vary only one of them, which is related to the growth rate of the healthy cells. For a determined critical value of this parameter, a Hopf bifurcation occurs in the equilibrium point representing the coexistence of the three types of cells (healthy cells, immune system cells and tumor cells), giving rise to the existence of a limit cycle. Studying the continuation of this limit cycle, we detect the occurrence of a cascade of period doubling bifurcations which, in the limit, leads to the chaotic behaviour of the solutions. In a second analysis, we vary two of the parameters of the model, representing the inactivation of the immune system cells by the tumor cells and the inactivation of the tumor cells by the immune system cells. In this analysis we determined certain parameter values for which the solutions having chaotic behavior tend to a regular regime, which is obtained by the calculation of the topological entropy, the Lyapunov exponents and predictability.