Results 121 to 130 of about 4,619,884 (143)

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
openaire   +2 more sources

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.
openaire   +1 more source

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
openaire   +1 more source

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
openaire   +3 more sources

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
openaire   +2 more sources

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  

Computation of the Center Isochronism Conditions for Polynomial Systems

Differential Equations, 2002
Romanovskii, V. G., Robnik, M.
openaire   +2 more sources

On the isochronism of the center of a system of nonlinear oscillations

1989
The author studies a system of differential equations of the form \(x'=y\), \(y'=P(x,y)\), \(P(0,0)=0\), where \(P(x,y)\) is a fourth degree polynomial. \textit{I. S. Kukles} [Dokl. Akad. Nauk SSSR 57, No. 4, 166 (1944)] found the necessary and sufficient conditions in order for the equilibrium point (0,0) of the system to be of a center type.
openaire   +2 more sources

Bifurcation of Limit Cycles and Isochronous Centers on Center Manifolds for a Class of Cubic Kolmogorov Systems in $${\mathbb {R}}^{3}$$

Qualitative Theory of Dynamical Systems, 2023
Wentao Huang
exaly  

The number of limit cycles bifurcating from the periodic orbits of an isochronous center

Mathematical Methods in the Applied Sciences, 2019
Sabrina Badi
exaly