Results 1 to 10 of about 121 (68)
Global phase portraits of quintic reversible uniform isochronous centers
Electronic Journal of Qualitative Theory of Differential EquationsThis paper studies the global phase portraits of uniform isochronous quintic centers at the origin with time reversibility such that their nonlinear part is not homogeneous.
Lina Guo, Aiyong Chen
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Phase Portraits of Uniform Isochronous Centers with Homogeneous Nonlinearities [PDF]
Journal of Dynamical and Control Systems, 2021 We classify the phase portraits in the Poincaré disc of the differential equations of the form x' = - y + xf(x, y), ẏ = x + yf(x, y) where f(x,y) is a homogeneous polynomial of degree n - 1 when n = 2, 3, 4, 5, and f has only simple zeroes. We also provide some general results on these uniform isochronous centers for all n ≥ 2.
Llibre, Jaume, Valls, Claudia
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Phase portraits of uniform isochronous quartic centers
Journal of Computational and Applied Mathematics, 2021 Agraïments: The first author is supported by a Ciência sem Fronteiras-CNPq grant number 201002/2012-4 ; grant UNAB13-4E-1604, and a CAPES grant 88881. 030454/2013-01do Programa CSF-PVE. In this paper we classify the global phase portraits in the Poincaré disc of all quartic polynomial differential systems with a uniform isochronous center at the origin
Jackson Itikawa, Jaume Llibre
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Limit Cycles Coming from Some Uniform Isochronous Centers [PDF]
Advanced Nonlinear Studies, 2016 Abstract This article is about the weak 16th Hilbert problem, i.e. we analyze how many limit cycles can bifurcate from the periodic orbits of a given polynomial differential center when it is perturbed inside a class of polynomial differential systems. More precisely, we consider the uniform isochronous centers
Haihua Liang +2 more
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Centers and Uniform Isochronous Centers of Planar Polynomial Differential Systems [PDF]
Journal of Dynamics and Differential Equations, 2018 For planar polynomial vector fields of the form \[ (-y X(x,y)) x (x Y(x,y)) y, \] where X and Y start at least with terms of second order in the variables x and y, we determine necessary and sufficient conditions under which the origin is a center or a uniform isochronous centers.
Jaume Llibre +3 more
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Discrete and Continuous Dynamical Systems - Series B, 2015 Agraïments: The first author is is supported by a Ciência sem Fronteiras-CNPq grant number 201002/ 2012-4. A CAPES grant number 88881.030454/2013-01 from the program CSF-PVE We classify the global phase portraits in the Poincar\'e disc of the differential systems =-y xf(x,y), =x yf(x,y), where f(x,y) is a homogeneous polynomial of degree 3.
Itikawa, Jackson, Llibre, Jaume
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Uniform isochronous cubic and quartic centers: Revisited
Journal of Computational and Applied Mathematics, 2017 In this paper we completed the classification of the phase portraits in the Poincaré disc of uniform isochronous cubic and quartic centers previously studied by several authors. There are three and fourteen different topological phase portraits for the uniform isochronous cubic and quartic centers respectively.
Artés Ferragud, Joan Carles +2 more
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Limit cycles in uniform isochronous centers of discontinuous differential systems with four zones
Discrete & Continuous Dynamical Systems - B, 2021 We apply the averaging theory of first order for discontinuous differential systems to study the bifurcation of limit cycles from the periodic orbits of the uniform isochronous center of the differential systems ẋ = -y+x, y = x + xy, and ẋ = -y + xy, y = x + xy, when they are perturbed inside the class of all discontinuous quadratic and cubic ...
Itikawa, Jackson +3 more
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UNIFORM ISOCHRONOUS CENTER OF HIGHER-DEGREE POLYNOMIAL DIFFERENTIAL SYSTEMS
Journal of Applied Analysis & Computation, 2023 Summary: In this paper, we study the uniform isochronous center of a class of more general higher-degree of polynomial differential systems and give the necessary and sufficient conditions for the origin point to be a center. At the same time, we illustrate that under some restrictions, the composition conjecture about these differential systems is ...
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Limit cycles for continuous and discontinuous perturbations of uniform isochronous cubic centers
Journal of Computational and Applied Mathematics, 2015 Agraïments: FEDER-UNAB10-4E-378. The second author is supported by a Ciência sem Fronteiras-CNPq grant number 201002/2012-4. Let p be a uniform isochronous cubic polynomial center. We study the maximum number of small or medium limit cycles that bifurcate from p or from the periodic solutions surrounding p respectively, when they are perturbed, either ...
Jaume Llibre, Jackson Itikawa
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