On the number of limit cycles for discontinuous piecewise linear differential systems in R^2n with two zones
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Rong, Feng (Shanghai Jiao Tong University. Department of Mathematics)

Date:	2013
Abstract:	We study the number of limit cycles of the discontinuous piecewise linear differential systems in R2n with two zones separated by a hyperplane. Our main result shows that at most (8n−6)n−1 limit cycles can bifurcate up to first-order expansion of the displacement function with respect to a small parameter. For proving this result we use the averaging theory in a form where the differentiability of the system is not necessary.
Grants:	Ministerio de Ciencia y Tecnología MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
Note:	Agraïments: The second author is partially supported by grant 11001172 from the National Natural Science Foundation of China and grant 20100073120067 from the Research Fund for the Doctoral Program of Higher Education of China.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Limit cycles, averaging method ; Discontinuous piecewise linear differential systems
Published in:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 23 Núm. 2 (2013) , p. 1350024, ISSN 1793-6551

DOI: 10.1142/S0218127413500247

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