Results 21 to 30 of about 4,619,884 (143)

A new method to determine isochronous center conditions for polynomial differential systems [PDF]

, 2003
The computation of period constants is a way to study isochronous center for polynomial differential systems. In this article, a new method to compute period constants is given.
Liu, Yirong, Huang, Wentao
core   +1 more source

Centers and isochronous centers for generalized quintic systems

Journal of Computational and Applied Mathematics, 2015
In this paper we classify the centers and the isochronous centers of certain polynomial differential systems in R2 of degree d ≥ 5 odd that incomplex notation can be written as z˙ = (λ + i)z + (zz¯)d-52 (Az5 + Bz4z¯ + Cz3z¯2 + Dz2z¯3 + Ezz¯4 + Fz¯5),where λ ∈ R and A, B, C, D, E, F ∈ C.
Jaume Giné, Jaume Llibre, Cláudia Valls   +2 more
openaire   +5 more sources

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, Rafael Ramírez, Valentín Ramírez, Natalia Sadovskaia   +3 more
openaire   +6 more sources

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
openaire   +3 more sources

Global isochronous potentials

, 2013
We present a geometric characterization of the nonlinear smooth functions V:R→R for which the origin is a global isochronous center for the scalar equation x ̈=−V′(x) .
Zampieri Gaetano, GORNI, Gianluca
core   +2 more sources

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.
Joan C. Artés, Jackson Itikawa, Jaume Llibre   +2 more
openaire   +4 more sources

Lie algebras and geometric complexity of an isochronous center condition [PDF]

, 2018
International audienceUsing the mould formalism introduced by Jean Ecalle, we define and study the geometric complexity of an isochronous center condition. The role played by several Lie ideals is discussed coming from the interplay between the universal
Cresson, Jacky, Palafox, Jordy
core   +2 more sources

Phase portraits of uniform isochronous quartic centers

Journal of Computational and Applied Mathematics, 2015
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 such that their nonlinear part is not homogeneous.
Jackson Itikawa, Jaume Llibre
openaire   +4 more sources

Periodic oscillators, isochronous centers and resonance [PDF]

Nonlinearity, 2019
Abstract An oscillator is called isochronous if all motions have a common period. When the system is forced by a time-dependent perturbation with the same period the dynamics may change and the phenomenon of resonance can appear. In this context, resonance means that all solutions are unbounded.
Rafael Ortega, David Rojas
openaire   +5 more sources

Persistent fluctuations in stride intervals under fractal auditory stimulation [PDF]

, 2014
Copyright @ 2014 Marmelat et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and ...
Beek, P.J., Beek, PJ, Andreas Daffertshofer, Kjerstin Torre (355432), Beek Peter J., Daffertshofer, A.; id_orcid, Vivien Marmelat (540065), Daffertshofer, Andreas, Torre Kjerstin, Kjerstin Torre, Marmelat, V, Torre, K, Marmelat Vivien, Marmelat, Vivien, Daffertshofer, A, Beek, P.J.; id_orcid, Torre, K., Peter J Beek, Daffertshofer Andreas, Vivien Marmelat, Beek, Peter J., Peter J. Beek (307441), Torre, Kjerstin, Marmelat, V.C.M., Andreas Daffertshofer (238842), Daffertshofer, A.   +25 more
core   +3 more sources