Results 21 to 30 of about 9,183,192 (276)
The point charge oscillator: qualitative and analytical investigations
Mathematical Modelling and Analysis, 2019 We study the mathematical model of the point charge oscillator which has been derived by A. Beléndez et al. [2]. First we determine the global phase portrait of this model in the Poincaré disk.
Klaus R. Schneider
doaj +1 more source
Global phase portraits of the generalized van der Pol systems
Bulletin des Sciences Mathématiques, 2023 We consider the generalized van der Pol systems x˙ = y, y˙ = -x + (1-x) f(y), where f ∈ R[y]. The classical van der Pol systems have f(y) = y. We first characterize when the origin of the generalized van der Pol systems is a center, and second we provide the global phase portraits in the Poincaré disc of the generalized van der Pol when f(y) = ay + ay ...
Jaume Llibre, Claudia Valls
openaire +4 more sources
Classification of Global Phase Portraits of a System of Liénard Type
Journal of Mathematical Analysis and Applications, 1995 This paper concerns a classification of global phase portraits generated by a Liénard differential equation, the two functions of which satisfy conditions called ``deformed mirror symmetry'' for the phase trajectories. These conditions lead to non-dissipative trajectories, for which the authors define separatrices limiting regions of the phase plane ...
Sugie, J., Hara, T.
openaire +1 more source
Bifurcation Diagrams and Global Phase Portraits for Some Hamiltonian Systems with Rational Potentials [PDF]
International Journal of Bifurcation and Chaos, 2018 In this paper, we study the global dynamical behavior of the Hamiltonian system [Formula: see text], [Formula: see text] with the rational potential Hamiltonian [Formula: see text], where [Formula: see text] and [Formula: see text] are polynomials of degree 1 or 2.
Ting Chen 0005, Jaume Llibre
openaire +4 more sources
Global Phase Portraits for the Kukles Systems of Degree 3 with ℤ2-Reversible Symmetries
International Journal of Bifurcation and Chaos, 2021 We provide the normal forms, the bifurcation diagrams and the global phase portraits on the Poincaré disk of all planar Kukles systems of degree [Formula: see text] with [Formula: see text]-symmetries.
Fabio Scalco Dias +2 more
openaire +2 more sources
Global Analysis of a Liénard System with Quadratic Damping
Discrete Dynamics in Nature and Society, 2018 In this paper, the global analysis of a Liénard equation with quadratic damping is studied. There are 22 different global phase portraits in the Poincaré disc.
Feng Guo
doaj +1 more source
Singular points and limit cycles of the generalized Kukles polynomial differential system
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2022 Background. Searching of numbers of Poincare limit cycles of polynomial dynamic systems belongs to second part of the 16th Gilbert problem, which is not solved in general.
I.N. Mal'kov, V.V. Machulis
doaj +1 more source
Combining global and multi-scale features in a description of the solar wind-magnetosphere coupling [PDF]
Annales Geophysicae, 2003 The solar wind-magnetosphere coupling during substorms exhibits dynamical features in a wide range of spatial and temporal scales. The goal of our work is to combine the global and multi-scale description of magnetospheric dynamics in a unified ...
A. Y. Ukhorskiy +4 more
doaj +1 more source
Time-Optimal Problem in the Roto-Translation Group with Admissible Control in a Circular Sector
Mathematics, 2023 We study a time-optimal problem in the roto-translation group with admissible control in a circular sector. The problem reveals the trajectories of a car model that can move forward on a plane and turn with a given minimum turning radius.
Alexey Mashtakov, Yuri Sachkov
doaj +1 more source
GLOBAL PHASE PORTRAITS OF SOME REVERSIBLE CUBIC CENTERS WITH COLLINEAR OR INFINITELY MANY SINGULARITIES [PDF]
International Journal of Bifurcation and Chaos, 2012 We study the reversible cubic vector fields of the form ẋ = -y + ax2+ bxy + cy2- y(x2+ y2), ẏ = x + dx2+ exy + fy2+ x(x2+ y2), having simultaneously a center at infinity and at the origin. In this paper, the subclass of these reversible systems having collinear or infinitely many singularities are classified with respect to topological equivalence.
Magdalena Caubergh +2 more
openaire +5 more sources