Journal
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Volume 25, Issue 11, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127415501448
Keywords
Discontinuous differential system; limit cycle; piecewise linear differential system
Funding
- MINECO/FEDER [MTM2008-03437, MTM2013-40998-P]
- AGAUR [2014SGR-568]
- ICREA Academia
- FP7-PEOPLE-IRSES [318999, 316338]
- FEDER-UNAB [10-4E-378]
- FAPESP-BRAZIL [2013/16492-0, 2012/18780-0]
- CAPES CSF-PVE from the program CSF-PVE [88881.030454/201301]
- Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP) [12/18780-0] Funding Source: FAPESP
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We study a class of discontinuous piecewise linear differential systems with two zones separated by the straight line x = 0. In x > 0, we have a linear saddle with its equilibrium point living in x > 0, and in x < 0 we have a linear differential center. Let p be the equilibrium point of this linear center, when p lives in x < 0, we say that it is real, and when p lives in x > 0 we say that it is virtual. We assume that this discontinuous piecewise linear differential system formed by the center and the saddle has a center q surrounded by periodic orbits ending in a homoclinic orbit of the saddle, independent if p is real, virtual or p is in x = 0. Note that q = p if p is real or p is in x = 0. We perturb these three classes of systems, according to the position of p, inside the class of all discontinuous piecewise linear differential systems with two zones separated by x = 0. Let N be the maximum number of limit cycles which can bifurcate from the periodic solutions of the center q with these perturbations. Our main results show that N = 2 when p is on x = 0, and N >= 2 when p is a real or virtual center. Furthermore, when p is a real center we found an example satisfying N >= 3.
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