Discontinuous and continuous dynamical systems

• Grant number: 13/15941-5
• Support Opportunities: Regular Research Grants
• Start date: October 01, 2013
• End date: September 30, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Maurício Firmino Silva Lima
• Grantee: Maurício Firmino Silva Lima
• Host Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Santo André , SP, Brazil
• City of the host institution: Santo André

Abstract

In the first part of this project we consider families of Differential Equations in a neighborhood of an isolated and degenerate equilibriumpoint. We consider issues such as the existence and persistence of families of periodic solutions and/or homoclinic.In the second part of the project we consider families of Differential Equations that are discontinuous (in general discontinuous perturbations of continuous linear vector fields ). We consider issues such as the bifurcation of limit cycles and the existence of homoclinic and/or heteroclinic connections. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

LIMA, MAURICIO F. S.; LLIBRE, JAUME; VALLS, CLAUDIA. Integrability of the Rucklidge system. NONLINEAR DYNAMICS, v. 77, n. 4, p. 1441-1453, SEP 2014. (13/15941-5)

SILVA LIMA, MAURICIO FIRMINO; PESSOA, CLAUDIO; PEREIRA, WEBER F.. On the Limit Cycles for a Class of Continuous Piecewise Linear Differential Systems with Three Zones. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 25, n. 4, APR 2015. (13/15941-5, 11/13152-8)

SILVA LIMA, MAURICIO FIRMINO; PESSOA, CLAUDIO; PEREIRA, WEBER F.. Limit Cycles Bifurcating from a Period Annulus in Continuous Piecewise Linear Differential Systems with Three Zones. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 27, n. 2, FEB 2017. (13/15941-5)