Results 41 to 50 of about 1,285,867 (186)

Normal forms and hyperbolic algebraic limit cycles for a class of polynomial differential systems

Electronic Journal of Differential Equations, 2018
We study the normal forms of polynomial systems having a set of invariant algebraic curves with singular points. We provide sufficient conditions for the existence of hyperbolic algebraic limit cycles.
Jaume Llibre, Claudia Valls
doaj  

Nests of limit cycles in quadratic systems

Advances in Nonlinear Analysis
We give a proof of the distribution property of limit cycles in so-called quadratic systems. We prove that the possible limit cycle distributions are either (n,0)\left(n,0) or (n,1)\left(n,1) (where n∈{0}∪Nn\in \left\{0\right\}\cup {\mathbb{N}}). The aim
Zegeling André
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Fourteen Limit Cycles in a Seven-Degree Nilpotent System

Abstract and Applied Analysis, 2013
Center conditions and the bifurcation of limit cycles for a seven-degree polynomial differential system in which the origin is a nilpotent critical point are studied. Using the computer algebra system Mathematica, the first 14 quasi-Lyapunov constants of
Wentao Huang, Ting Chen, Tianlong Gu
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Rapid evolution of complex limit cycles [PDF]

, 2009
The current article studies certain problems related to complex cycles of holomorphic foliations with singularities in the complex plane. We focus on the case when polynomial differential one-form gives rise to a foliation by Riemann surfaces.
Dimitrov, Nikolay
core  

Realization problems for limit cycles of planar polynomial vector fields [PDF]

, 2015
We show that for any finite configuration of closed curves $\Gamma\subset \mathbb{R}^2$, one can construct an explicit planar polynomial vector field that realizes $\Gamma$, up to homeomorphism, as the set of its limit cycles with prescribed periods ...
Margalef-Bentabol, Juan, Peralta-Salas, Daniel   +1 more
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From limit cycles to strange attractors

, 2010
We define a quantitative notion of shear for limit cycles of flows. We prove that strange attractors and SRB measures emerge when systems exhibiting limit cycles with sufficient shear are subjected to periodic pulsatile drives.
B.R. Hunt, B.R. Hunt, G.A. Gottwald, I. Falconer, K.K. Lin, L.-S. Young, L.-S. Young, M. Benedicks, M. Benedicks, M.V. Jakobson, Mikko Stenlund, P. Thieullen, Ph. Thieullen, Q. Wang, Q. Wang, Q. Wang, Q. Wang, R.E.L. DeVille, W. Ott, W. Tucker, William Ott   +20 more
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Resonant Motions of Dynamic Offshore Structures in Large Waves

Fluids, 2021
In marine engineering, the dynamics of fixed offshore structures (for oil and gas production or for wind turbines) are normally found by modelling of the motion by a classical mass-spring damped system.
Ove Tobias Gudmestad
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Multiplicity of Limit Cycle Attractors in Coupled Heteroclinic Cycles

, 2002
A square lattice distribution of coupled oscillators that have heteroclinic cycle attractors is studied. In this system, we find a novel type of patterns that is spatially disordered and periodic in time.
Tachikawa, Masashi
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Coexistence of Algebraic Limit Cycles and Small Limit Cycles of Two Classes of Near-Hamiltonian Systems with a Nilpotent Singular Point

Axioms
In this paper, two classes of near-Hamiltonian systems with a nilpotent center are considered: the coexistence of algebraic limit cycles and small limit cycles.
Huimei Liu, Meilan Cai, Feng Li
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Few-Body Effects in Cold Atoms and Limit Cycles

, 2006
Physical systems with a large scattering length have universal properties independent of the details of the interaction at short distances. Such systems can be realized in experiments with cold atoms close to a Feshbach resonance. They also occur in many
Bedaque, Bedaque, Bedaque, Braaten, Braaten, Braaten, Braaten, Braaten, Braaten, Efimov, Esry, H.-W. Hammer, Jonsell, Kraemer, Nielsen, Platter, Platter, Wilson, Yamashita, Yamashita   +19 more
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