Results 11 to 20 of about 366,422 (303)

Chemical Systems with Limit Cycles. [PDF]

Bull Math Biol, 2023
AbstractThe dynamics of a chemical reaction network (CRN) is often modeled under the assumption of mass action kinetics by a system of ordinary differential equations (ODEs) with polynomial right-hand sides that describe the time evolution of concentrations of chemical species involved. Given an arbitrarily large integer $$K \in {\mathbb N}$$
Erban R, Kang HW.
europepmc   +8 more sources

Friction generated limit cycles [PDF]

IEEE Transactions on Control Systems Technology, 2001
This paper treats limit cycles caused by friction. The goal has been to explain phenomena that have been observed experimentally in mechatronic systems. Experiments have shown that oscillations of qualitatively different types can be obtained simply by changing controller specifications. Stiction is important in some cases but not in others.
K J Åström
exaly   +5 more sources

Limit cycles and chaos in the hybrid atom-optomechanics system. [PDF]

Sci Rep, 2022
We consider atoms in two different periodic potentials induced by different lasers, one of which is coupled to a mechanical membrane via radiation pressure force.
Xu X, Krisnanda T, Liew TCH.
europepmc   +2 more sources

Rational Limit Cycles on Abel Polynomial Equations

Mathematics, 2020
In this paper we deal with Abel equations of the form d y / d x = A 1 ( x ) y + A 2 ( x ) y 2 + A 3 ( x ) y 3 , where A 1 ( x ) , A 2 ( x ) and A 3 ( x ) are real polynomials and A 3 ≢ 0 .
Claudia Valls
exaly   +3 more sources

Limit Cycles for the Kukles system [PDF]

Journal of Dynamical and Control Systems, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zang, Hong, Zhang, Tonghua, Tian, Yu-Chu, Tade, Moses O.   +3 more
openaire   +4 more sources

Exploring Limit Cycles of Differential Equations through Information Geometry Unveils the Solution to Hilbert's 16th Problem. [PDF]

Entropy (Basel)
The detection of limit cycles of differential equations poses a challenge due to the type of the nonlinear system, the regime of interest, and the broader context of applicable models.
da Silva VB, Vieira JP, Leonel ED.
europepmc   +2 more sources

On limit cycles of autonomous systems

Современная математика: Фундаментальные направления
We consider the problem of the existence of limit cycles for autonomous systems of differential equations. We present quite elementary considerations that can be useful in discussing qualitative issues that arise in the course of ordinary differential ...
T. M. Ivanova, A. B. Kostin, A. I. Rubinshtein, V. B. Sherstyukov   +3 more
doaj   +2 more sources

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
doaj   +2 more sources

The Cell Cycle is a Limit Cycle [PDF]

Mathematical Modelling of Natural Phenomena, 2012
Progression along the successive phases of the mammalian cell cycle is driven by a network of cyclin-dependent kinases (Cdks). This network is regulated by a variety of negative and positive feedback loops. We previously proposed a detailed, 39-variable model for the Cdk network and showed that it is capable of temporal self-organization in the form of
Gérard, Claude, Goldbeter, Albert
openaire   +2 more sources

The algebraic curves of planar polynomial differential systems with homogeneous nonlinearities

Electronic Journal of Qualitative Theory of Differential Equations, 2021
We consider planar polynomial systems of ordinary differential equations of the form $\dot x = x + P_n(x,y)$, $\dot y = y + Q_n(x,y)$, where $P_n(x,y),\ Q_n(x,y)$ are homogeneous polynomials of degree $n$.
Vladimir Cheresiz, Evgenii Volokitin
doaj   +1 more source