Electron. J. Diff. Equ., Vol. 2015 (2015), No. 228, pp. 1-12.

Arbitrary number of limit cycles for planar discontinuous piecewise linear differential systems with two zones

Denis de Carvalho Braga, Luis Fernando Mello

Abstract:
For any given positive integer n we show the existence of a class of discontinuous piecewise linear differential systems with two zones in the plane having exactly n hyperbolic limit cycles. Moreover, all the points on the separation boundary between the two zones are of sewing type, except the origin which is the only equilibrium point.

Submitted April 28, 2015. Published September 02, 2015.
Math Subject Classifications: 34C05, 34C25, 37G10.
Key Words: Piecewise linear differential system; limit cycle; non-smooth differential system.

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Denis de Carvalho Braga
Instituto de Matemática e Computação
Universidade Federal de Itajubá
Avenida BPS 1303, Pinheirinho, CEP 37.500-903
Itajubá, MG, Brazil
email: braga@unifei.edu.br
Luis Fernando Mello
Instituto de Matemática e Computação
Universidade Federal de Itajubá
Avenida BPS 1303, Pinheirinho, CEP 37.500-903
Itajubá, MG, Brazil
Tel: 00-55-35-36291217, Fax: 00-55-35-36291140
email: lfmelo@unifei.edu.br

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