Chaos in mathematical models of cancer - how and why it occurs. An approach from the point of view of Bio-Mathematics

• Grant number: 12/07694-5
• Support Opportunities: Scholarships in Brazil - Master
• Start date: July 01, 2012
• End date: April 30, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Marcelo Messias
• Grantee: Patrícia Demétria Branco da Silva
• Host Institution: Faculdade de Ciências e Tecnologia (FCT). Universidade Estadual Paulista (UNESP). Campus de Presidente Prudente. Presidente Prudente , SP, Brazil

Abstract

The use of mathematical models in the study of tumour growth is increasing in the last decades. Several models proposed in the literatura are based in Lotka-Volterra type systems of competition, cooperation and prey-predator and their solutions present chaotic dynamics. We aim to study the mathematical tools used to explain the occurence of chaos in these models, mainly the qualitative theory and bifurcations of ordinary differential equations, in order to understand o why and how this behaviour occurs. Based on this study we intend to relate the chaotic dynamics with biological characteristics of the model in order to better understand the developing of this disease and possibly its control.

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

SILVA, Patrícia Demétria Branco da. Comportamento caótico em modelos matemáticos de câncer. 2014. Master's Dissertation - Universidade Estadual Paulista (Unesp). Faculdade de Ciências e Tecnologia. Presidente Prudente Presidente Prudente.