Academic Journal
Simultaneous occurrence of sliding and crossing limit cycles in piecewise linear planar vector fields
| العنوان: | Simultaneous occurrence of sliding and crossing limit cycles in piecewise linear planar vector fields |
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| المؤلفون: | Cardoso, Joäo L., Llibre, Jaume, Novaes, Douglas D., Tonon, Durval José |
| سنة النشر: | 2020 |
| المجموعة: | Universitat Autònoma de Barcelona: Dipòsit Digital de Documents de la UAB |
| مصطلحات موضوعية: | Non-smooth differential system, Limit cycle, Piecewise linear differential system |
| الوصف: | In the present study, we consider planar piecewise linear vector fields with two zones separated by the straight line x = 0. Our goal is to study the existence of simultaneous crossing and sliding limit cycles for such a class of vector fields. First, we provide a canonical form for these systems assuming that each linear system has centre, a real one for y<0 and a virtual one for y>0, and such that the real centre is a global centre. Then, working with a first-order piecewise linear perturbation we obtain piecewise linear differential systems with three crossing limit cycles. Second, we see that a sliding cycle can be detected after a second-order piecewise linear perturbation. Finally, imposing the existence of a sliding limit cycle we prove that only one adittional crossing limit cycle can appear. Furthermore, we also characterize the stability of the higher amplitude limit cycle and of the infinity. The main techniques used in our proofs are the Melnikov method, the Extended Chebyshev systems with positive accuracy, and the Bendixson transformation. |
| نوع الوثيقة: | article in journal/newspaper |
| وصف الملف: | application/pdf |
| اللغة: | English |
| تدمد: | 14689367 14689375 |
| Relation: | Ministerio de EconomÃa y Competitividad MTM2016-77278-P; Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617; European Commission 777911; Dynamical Systems; vol. 35 3 (February 2020) p. 490-514; https://ddd.uab.cat/record/221365; urn:10.1080/14689367.2020.1722064; urn:oai:ddd.uab.cat:221365; urn:scopus_id:85079362908; urn:gsduab:4952; urn:wos_id:000513443200001; urn:articleid:14689375v35n3p490 |
| الاتاحة: | https://ddd.uab.cat/record/221365 |
| Rights: | open access ; Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permÃs del(s) titular(s) de drets. ; https://rightsstatements.org/vocab/InC/1.0/ |
| رقم الانضمام: | edsbas.26BE00AC |
| قاعدة البيانات: | BASE |
| تدمد: | 14689367 14689375 |
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