<p class="first last">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.</p> </div>
%0 Journal Article
%1 doi:10.1142/S0218127415501448
%A Llibre, Jaume
%A Novaes, Douglas D.
%A Teixeira, Marco A.
%D 2015
%J International Journal of Bifurcation and Chaos
%K myown published
%N 11
%P 1550144
%R 10.1142/S0218127415501448
%T Limit Cycles Bifurcating from the Periodic Orbits of a Discontinuous Piecewise Linear Differentiable Center with Two Zones
%U http://www.worldscientific.com/doi/abs/10.1142/S0218127415501448
%V 25
%X <p class="first last">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.</p> </div>
@article{doi:10.1142/S0218127415501448,
abstract = { <p class="first last">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.</p> </div>},
added-at = {2015-12-28T06:19:24.000+0100},
author = {Llibre, Jaume and Novaes, Douglas D. and Teixeira, Marco A.},
biburl = {https://www.bibsonomy.org/bibtex/2247d121db85a72856b81ff681dedd867/ddnovaes},
doi = {10.1142/S0218127415501448},
eprint = {http://www.worldscientific.com/doi/pdf/10.1142/S0218127415501448},
interhash = {79606a56200d4da8dccc82cf46c2e959},
intrahash = {247d121db85a72856b81ff681dedd867},
journal = {International Journal of Bifurcation and Chaos},
keywords = {myown published},
number = 11,
pages = 1550144,
timestamp = {2015-12-28T06:19:24.000+0100},
title = {Limit Cycles Bifurcating from the Periodic Orbits of a Discontinuous Piecewise Linear Differentiable Center with Two Zones},
url = {http://www.worldscientific.com/doi/abs/10.1142/S0218127415501448},
volume = 25,
year = 2015
}