Results 1 to 10 of about 6,858 (137)
Periodic oscillators, isochronous centers and resonance [PDF]
Nonlinearity, 2021 28 ...
Rafael Ortega, David Rojas
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Center conditions for a simple class of quintic systems [PDF]
International Journal of Mathematics and Mathematical Sciences, 2002 We obtained center conditions for an O-symmetric system of degree 5 for which the origin is a uniformly isochronous singular point.
Evgenii P. Volokitin
doaj +7 more sources
On the Shape of Limit Cycles That Bifurcate from Isochronous Center [PDF]
The Scientific World Journal, 2014 New idea and algorithm are proposed to compute asymptotic expression of limit cycles bifurcated from the isochronous center. Compared with known inverse integrating factor method, new algorithm to analytically computing shape of limit cycle proposed in ...
Guang Chen, Yuhai Wu
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Uniformly isochronous polynomial centers
Electronic Journal of Differential Equations, 2005 We study a specific family of uniformly isochronous polynomial systems. Our results permit us to solve a problem about centers of such systems. We consider the composition conjecture for uniformly isochronous polynomial systems.
Vladimir V. Ivanov, Evgenii P. Volokitin
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Limit Cycles and Integrability of a Class of Quintic System
Mathematics, 2022 In this paper, a class of quintic systems is investigated. The first 13 focal values are computed with the aid of MATHEMATICA. Then the necessary conditions of integrability and linearizability are obtained and the sufficiency of every condition is ...
Yanli Tang, Dongmei Zhang, Feng Li
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On the analytic commutator for $\Lambda$−$\Omega$ differential systems
Electronic Journal of Qualitative Theory of Differential Equations, 2023 In this paper, we give the necessary and sufficient conditions for some $\Lambda$−$\Omega$ differential systems to have an analytic commutator, use these properties to judge the origin point of the $\Lambda$−$\Omega$ differential systems to be an ...
Zhengxin Zhou
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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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A survey of isochronous centers [PDF]
Qualitative Theory of Dynamical Systems, 1999 In this survey we give an overview of the results obtained in the study of isochronous centers of vector fields in the plane. This paper consists of two parts. In the first one (sections 2--8), we review some general techniques that proved to be useful in the study of isochronicity.
Sabatini, Marco, J. Chavarriga
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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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Quadratic Isochronous centers commute [PDF]
Applicationes Mathematicae, 1999 Summary: The author proves that every quadratic plane differential system having an isochronous center commutes with a polynomial differential system.
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