Linearly implicit Liénard systems |
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Authors: | Ricardo Riaza |
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Institution: | Departamento de Matemática Aplicada a las Tecnologías de la Información, Escuela Técnica Superior de Ingenieros de Telecomunicación, Universidad Politécnica de Madrid - 28040 Madrid, Spain |
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Abstract: | The presence of nonlinearities in the capacitance and the inductance in van der Pol type electrical circuits defines a linearly implicit (or quasilinear) counterpart of the classical Liénard systems. When the reactances remain positive, the existence of a unique attracting periodic solution follows, with minor modifications, as in the classical setting. Novel results are obtained when the values of reactances may vanish at certain points of the state space; these points yield singularities of the model, and the existence of an attracting periodic solution can be characterized in terms of the behavior of certain smooth solutions crossing the singular manifold through so-called I-singularities. |
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Keywords: | 34A09 34C25 37C27 94C05 |
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