Dynamics and bifurcations of fields polynomial vector in R3 with a cylinder invariant

Author(s)

Naiara Aparecida dos Santos Silva

• Document type: Master's Dissertation
• Press: Presidente Prudente. 2016-11-08.
• Institution: Universidade Estadual Paulista (Unesp). Faculdade de Ciências e Tecnologia. Presidente Prudente
• Defense date: 2016-09-16
• Advisor: Marcelo Messias

Abstract

In this work we study a class of quadratic polynomial differential systems defined in R3 which has a cylinder as invariant algebraic surface. More specifically, we study the stability and local bifurcations of singular points, using for this the structure of the phase space, that is, the geometric constraint provided by the existence of the invariant cylinder. We prove that there is a Hopf bifurcation on the cylinder, which leads to the creation of a stable limit cycle, for certain parameter values. We also show the existence of homoclinic orbits, heteroclinic orbits and centers, contained in these cylinders. These elements are key ingredients to understand the complicated dynamic behavior of small perturbations of these differential systems in R3. (AU)

• FAPESP's process: 14/14096-2 - Global dynamics and integrability of quadratic polynomial differential systems in R3 with symetry
• Grantee: Naiara Aparecida dos Santos Silva
• Support Opportunities: Scholarships in Brazil - Master