Equações Diferenciais por partes:ciclos limite e cones invaiantes
Data
2011-03-25
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Universidade Federal de Goiás
Resumo
In this work, we consider classes of discontinuous piecewise linear systems in the plane and continuous in the space. In the plane, we analyze systems of focus-focus (FF), focusparabolic (FP) and parabolic-parabolic (PP) type, separated by the straight line x = 0, and we prove that can appear until two limit cycles depending of parameters variations. Also we study a specific system, piecewise, with two saddles (one fixed in the origin and the other in the neighborhood of point (1;1)) separated by the straight line y= -x+1, and we show that can appear until two limit cycles depending of parameters variations. Finally, we examine a continuous piecewise linear system in R³ and we prove the existence of invariant cones and, through this structures, we determine some stable and unstable behavior.
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SILVA, Thársis Souza. Piecewise differential equation: limit cycles and invariant cones. 2011. 152 f. Dissertação (Mestrado em Ciências Exatas e da Terra) - Universidade Federal de Goiás, Goiânia, 2011.