The Markus-Yamabe conjecture does not hold for discontinuous piecewise linear differential systems separated by one straight line
The Markus-Yamabe conjecture is a conjecture on global asymptotic stability. The conjecture states that if a differentiable system x˙ = f(x) has a singularity and the Jacobian matrix Df(x) has everywhere eigenvalues with negative real part, then the singularity is a global attractor. In this paper w...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:221383 |
| Acceso en línea: | https://ddd.uab.cat/record/221383 https://dx.doi.org/urn:doi:10.1007/s10884-020-09825-8 |
| Access Level: | acceso abierto |
| Palabra clave: | Discontinuous differential system Limit cycle Markus-Yamabe conjecture |
| Sumario: | The Markus-Yamabe conjecture is a conjecture on global asymptotic stability. The conjecture states that if a differentiable system x˙ = f(x) has a singularity and the Jacobian matrix Df(x) has everywhere eigenvalues with negative real part, then the singularity is a global attractor. In this paper we consider discontinuous piecewise linear differential systems in R2 separated by one straight line Σ such that the unique singularity of the system is at Σ and the Jacobian matrix of the system has everywhere eigenvalues with negative real part. We prove that these discontinuous piecewise linear differential systems can have one crossing limit cycle and consequently these systems do not satisfy the Markus-Yamabe conjecture. |
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