Averaging Theory for studying the periodic solutions of the differential systems a...
Regularization of planar Filippov Systems near a codimension one singularity
Grant number: | 12/06879-1 |
Support Opportunities: | Regular Research Grants |
Duration: | June 01, 2012 - May 31, 2014 |
Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Geometry and Topology |
Principal Investigator: | Ricardo Miranda Martins |
Grantee: | Ricardo Miranda Martins |
Host Institution: | Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil |
Abstract
The theory of Non-Smooth Dynamical Systems is a subject that has been developing very fast in recent years, mainly due to its strong relationship with other fields of science. Establish clear notions of stability and bifurcations that are consistent with the real world has been an arduous and challenging task for mathematicians, physicists and engineers. There is very little done with respect to the study of generic bifurcations and normal forms for such systems.Our goal is to study is a non-smooth version of Hilbert's 16th problem for discontinuous systems, mainly studying the birth of limit cycles when considering non-smooth perturbations of linear smooth centers. The existence of such orbits is of fundamental importance in physical models based on discontinuous equations.The basic tool in this study is the Averaging Method. which applies almost directly to the non-smooth systems. In particular, we also show that the averaged equation is compatible with the discontinuity line of the system. (AU)
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