Results 121 to 130 of about 1,422 (148)

Bifurcation of Critical Periods from a Quartic Isochronous Center

International Journal of Bifurcation and Chaos, 2014
This paper is focused on the bifurcation of critical periods from a quartic rigidly isochronous center under any small quartic homogeneous perturbations. By studying the number of zeros of the first several terms in the expansion of the period function in ε, it shows that under any small quartic homogeneous perturbations, up to orders 1 and 2 in ε ...
Linping Peng, Zhaosheng Feng
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BIFURCATION OF LIMIT CYCLES AND ISOCHRONOUS CENTERS FOR A QUARTIC SYSTEM

International Journal of Bifurcation and Chaos, 2013
For a quartic polynomial system we investigate bifurcations of limit cycles and obtain conditions for the origin to be a center. Computing the singular point values we find also the conditions for the origin to be the eighth order fine focus. It is proven that the system can have eight small amplitude limit cycles in a neighborhood of the origin.
Wentao Huang, Aiyong Chen, Qiujin Xu
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Generalized isochronous centers for complex systems

Acta Mathematica Sinica, English Series, 2010
The authors consider complex polynomial systems with complex time. Definitions of generalized isochronous centers and period constants are given, and an algorithm is obtained to compute generalized period constants. The method is applied to a class of real cubic Kolmogorov systems.
Wang, Qin Long, Liu, Yi Rong
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Isochronous centers and flat Finsler metrics (I)

Canadian Journal of Mathematics
AbstractThe local structure of rotationally symmetric Finsler surfaces with vanishing flag curvature is completely determined in this paper. A geometric method for constructing such surfaces is introduced. The construction begins with a planar vector field X that depends on two functions of one variable.
Xinhe Mu, Hui Miao, Libing Huang
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Centers and Isochronous Centers of Newton Systems with Force Function Quadratic in Velocities

Differential Equations, 2019
Necessary and sufficient conditions are obtained for a center as well as an isochronous center of holomorphic Newton equations with force function quadratic in velocities.
Amel'kin, V. V., Rudenok, A. E.
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Isochronous centers of cubic reversible systems

2008
In this paper we study isochronous centers of reversible two-dimensional autonomous system with linear part of center type and nonlinear part given by polynomials of third degree. Firstly we find necessary conditions for such isochronous centers in polar coordinates and finally we give a proof of the isochronicity of these systems using different ...
Javier Chavarriga, Isaac García
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Classification of the centers and isochronous centers for a class of quartic-like systems

Nonlinear Analysis: Theory, Methods & Applications, 2009
The authors classify the centers and isochronous centers for a class of polynomial differential equations in \(\mathbb R^2\) of degree \(d\) that can be written as \[ \dot z=iz+(z\bar z)^{\frac{d-4}{2}}(Az^3\bar z+Bz^2{\bar z}^2+C{\bar z}^4),\tag{1} \] where \(z = x + iy,\) \(d \geq4\) is an even, positive integer, and \(A, B, C\in\mathbb C\). The main
Llibre, Jaume, Valls, Clàudia
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Commutators and linearizations of isochronous centers

2000
The authors study isochronous centers of some classes of plane differential systems. They consider systems with constant angular speed, both with homogeneous and nonhomogeneous nonlinearities, and show how to construct linearizations and first integrals to such systems, if a commutator is known.
Sabatini, Marco, L. Mazzi
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The Uniform Isochronous Centers with Homogeneous Nonlinearities of Degree 5

Journal of Dynamical and Control Systems
The interest in studying the uniform isochronous centers goes back to C. Huygens in the XVII century. Since then, many papers have been published on this subject. In particular, the phase portraits of the polynomial uniform isochronous center up to degree four have been classified.
Dong, Guangfeng, Llibre, Jaume
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Bifurcation of limit cycles and isochronous centers on center manifolds for four‐dimensional systems

Mathematical Methods in the Applied Sciences, 2022
Qinlong Wang, Wentao Huang
exaly