The matching of two stable sewing linear systems in the plane

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• 作者：Denis de Carvalho Braga ^{braga@unifei.edu.br" class="auth_mail" title="E-mail the corresponding author} ; Alexander Fernandes da Fonseca ^{alexff@unifei.edu.br" class="auth_mail" title="E-mail the corresponding author} ; Luis Fernando Mello ; ^{lfmelo@unifei.edu.br" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Piecewise linear differential system ; Non-smooth differential system ; Global stability ; Hurwitz matrix
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：15 January 2016
• 年：2016
• 卷：433
• 期：2
• 页码：1142-1156
• 全文大小：565 K

文摘

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.