Results 141 to 150 of about 6,898 (176)

Isochronicity of centers at a center manifold

AIP Conference Proceedings, 2012
For a three dimensional system with a center manifold filled with closed trajectories (corresponding to periodic solutions of the system) we give criteria on the coefficients of the system to distinguish between the cases of isochronous and non-isochronous oscillations. Bifurcations of critical periods of the system are studied as well.
Brigita Ferčec, Matej Mencinger
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Isochronous Centers and Isochronous Functions

Acta Mathematicae Applicatae Sinica, English Series, 2002
The author investigates the isochronous centers of two classes of planar systems of ordinary differential equations: 1) Liénard systems of the form \((\dot x)=y-F(x),(\dot y)=-g(x)\), 2) Hamiltonian systems of the form \((\dot x)=-g(y)\), \((\dot y)=f(x)\), with emphasis on the case when the functions \(g\) or \(f\) are isochronous. For the first class
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Periodic perturbations of an isochronous center

Qualitative Theory of Dynamical Systems, 2002
The author discusses the possibility of producing resonance in a nonlinear isochronous center. In some cases it is shown than one can find periodic forcings (with the same period of the center) such that the solutions of the perturbed equation are unbounded.
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Rational Liénard Systems with a Center and an Isochronous Center

Differential Equations, 2020
The following Liénard system \[ \Dot{x}=-y,\quad\Dot{y}=f(x)+yg(x)\tag{1} \] is considered with rational functions \(f\) and \(g\), where the functions \(f\) and \(g\) are linearly independent and holomorphic, and \(f(0)=g(0)=0\) and \(f'(0)=1\). Firstly, the definition of degree of an element \(g(x)/h(x)\) of the field \(k(x)\) and the definition of ...
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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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Center and isochronous center problems for quasi analytic systems

Acta Mathematica Sinica, English Series, 2008
Consider the planar quasi-analytic systems \[ \begin{aligned} {dx\over dt} &=\delta x- y+ \sum^\infty_{k=2} (x^2+ y^2)^{(k-1)(\lambda- 1)/2}X_k(x,y),\\ {dy\over dt} &= x+\delta y+ \sum^\infty_{k=2} (x^2+ y^2)^{(k-1)(\lambda- 1)/2} Y_k(x, y),\end{aligned} \] where \[ \begin{aligned} X_k(x, y) &= \sum_{\alpha+\beta= k} A_{\alpha\beta} x^\alpha y^\beta,\\
Liu, Yi Rong, Li, Ji Bin
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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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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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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 ...
Peng, Linping, Feng, Zhaosheng
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Number of Critical Periods for Perturbed Rigidly Isochronous Centers

International Journal of Bifurcation and Chaos, 2016
This paper deals with the bifurcation of critical periods from a rigidly quartic isochronous center. It shows that under any small homogeneous perturbation of degree four, up to any order in [Formula: see text], there are at most two critical periods bifurcating from the periodic orbits of the unperturbed system, and the upper bound is sharp.
Lu, Lianghaolong, Peng, Linping, Feng, Zhaosheng   +2 more
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