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On the periodic solutions of the 5-dimensional Lorenz equation modeling coupled Rosby waves and gravity waves
https://ddd.uab.cat/record/182728
de Carvalho, TiagoThu, 07 Dec 2017 14:21:34 GMThttps://ddd.uab.cat/record/1827282017On Poincaré-Bendixson theorem and non-trivial minimal sets in planar nonsmooth vector fields
https://ddd.uab.cat/record/182685
In this paper some qualitative and geometric aspects of nonsmooth vector fields theory are discussed. A Poincaré-Bendixson Theorem for a class of nonsmooth systems is presented. In addition, a minimal set in planar Filippov systems not predicted in classical Poincaré-Bendixson theory and whose interior is non-empty is exhibited. The concepts of limit sets, recurrence, and minimal sets for nonsmoothsystems are defined and compared with the classical ones. Moreover some differences between them are pointed out. Buzzi, ClaudioTue, 05 Dec 2017 04:07:49 GMThttps://ddd.uab.cat/record/1826852018Limit cycles of discontinuous piecewise polynomial vector fields
https://ddd.uab.cat/record/182510
When the first average function is non-zero we provide an upper bound for the maximum number of limit cycles bifurcating from the periodic solutions of the center x= -y((x^2 y^2)/2)^m and y= x((x^2 y^2)/2)^m with m 1, when we perturb it inside a class of discontinuous piecewise polynomial vector fields of degree n with k pieces. The positive integers m, n and k are arbitrary. The main tool used for proving our results is the averaging theory for discontinuous piecewise vector fields. de Carvalho, TiagoTue, 28 Nov 2017 07:46:28 GMThttps://ddd.uab.cat/record/1825102017Bifurcation of limit cycle from a n-dimensional linear center inside a class of piecewise linear differential systems
https://ddd.uab.cat/record/150540
Let n be an even integer. We study the bifurcation of limit cycles from the periodic orbits of the n-dimensional linear center given by the differential system x˙ 1 = −x2, x˙ 2 = x1, . . . , x˙ n−1 = −xn, x˙ n = xn−1, perturbed inside a class of piecewise linear differential systems. Our main result shows that at most (4n − 6)n/2−1 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 needed. Cardin, Pedro T.Fri, 06 May 2016 08:49:23 GMThttps://ddd.uab.cat/record/1505402012Limit cycles of discontinuous piecewise linear differential systems
https://ddd.uab.cat/record/150439
We study the bifurcation of limit cycles from the periodic orbits of a two-dimensional (resp. four-dimensional) linear center in Rn perturbed inside a class of discontinuous piecewise linear differential systems. Our main result shows that at most 1 (resp. 3) limit cycle can bifurcate up to first-order expansion of the displacement function with respect to the small parameter. This upper bound is reached. For proving these results, we use the averaging theory in a form where the differentiability of the system is not needed. Cardin, Pedro ToniolFri, 06 May 2016 08:30:49 GMThttps://ddd.uab.cat/record/1504392011Detecting periodic orbits in some 3d chaotic quadratic polynomial differential systems
https://ddd.uab.cat/record/145300
Using the averaging theory we study the periodic solutions and their linear stability of the 3-dimensional chaotic quadratic polynomial differential systems without equilibria studied in [3]. All these differential systems depend only on one-parameter. de Carvalho, TiagoTue, 12 Jan 2016 16:38:07 GMThttps://ddd.uab.cat/record/1453002015