The Focus-Center-Limit Cycle Bifurcation in Discontinuous Planar Piecewise Linear Systems Without Sliding
Planar discontinuous piecewise linear systems with two linearity zones, one of them being of focus type, are considered. By using an adequate canonical form under certain hypotheses, the bifurcation of a limit cycle, when the focus changes its stability after becoming a linear center, is completely characterized. Analytic expressions for the amplitude, period and characteristic multiplier of the bifurcating limit cycle are provided. The studied bifurcation appears in real world applications, as shown with the analysis of an electronic Wien bridge oscillator without symmetry.
Authors acknowledge the fruitful suggestions of Prof. F. Torres on a preliminary version of the manuscript. They are partially supported by the Ministerio de Ciencia y Tecnología, Plan Nacional I+D+I, in the frame of projects MTM2009-07849, MTM2010-20907, MTM2012-31821, and by the Consejería de Educación y Ciencia de la Junta de Andalucía under grants TIC-0130 and P08-FQM-03770.
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