Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4614918 | Journal of Mathematical Analysis and Applications | 2016 | 15 Pages |
Abstract
In this article we study one of the main problems in the qualitative theory of planar differential equations: the problem of determining the basin of attraction of an equilibrium point. We give a rigorous proof that for planar sewing piecewise linear systems with two zones, defined by Hurwitz matrices the unique equilibrium point in the separation straight line is globally asymptotically stable. On the other hand, we prove that sewing piecewise linear systems with two zones in the plane, defined by Hurwitz matrices can have one unstable equilibrium point at the origin allowing a broken line to separate the zones, leading to counter-intuitive dynamical behaviors of simple piecewise linear systems in the plane.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Denis de Carvalho Braga, Alexander Fernandes da Fonseca, Luis Fernando Mello,