The cyclicity of the period annulus of a quadratic reversible system with a hemicycle
Discrete and Continuous Dynamical Systems, 2011 The cyclicity of the period annulus of a quadratic reversible and non-Hamiltonian system under quadratic perturbations is studied. The centroid curve method and other mathematical techniques are combined to prove that the related Abelian integral has at most two zeros. This gives a proof of Conjecture 1 in [8] for one case.
Linping Peng
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The cyclicity of the period annulus of a class of quadratic reversible system
Communications on Pure and Applied Analysis, 2012 In this paper, we study the bifurcation of limit cycles of a class of planar quadratic reversible system $\dot{x}=y+4x^2$, $\dot{y}=-x+2xy$ under quadratic perturbations. It is proved that the cyclicity of the period annulus is equal to two.
Yulin Zhao
exaly +2 more sources
The Cyclicity of the Period Annulus of the Quadratic Hamiltonian Systems with Non-Morsean Point
Journal of Differential Equations, 2000 This paper deals with the number of limit cycles for small quadratic perturbations of quadratic Hamiltonian systems with non-Morsean point, that is \[ \begin{aligned} \dot x&= 2xy+ \varepsilon \Bigl( \sum_{i+j\leq 2} a_{ij} (\varepsilon) x^i y^j\Bigr),\\ \dot y&= 6x+ 6x^2- y^2+ \varepsilon \Bigl( \sum_{i+j\leq 2} b_{ij} (\varepsilon) x^i y^j \Bigr ...
Yulin Zhao
exaly +3 more sources
Early comparison of one-year outcomes after aortic mechanical vs. biological valve replacement in Chinese patients with small aortic annulus [PDF]
Journal of Cardiothoracic SurgeryBackground This study compares short-term clinical and hemodynamic outcomes of AVR using mechanical versus bovine pericardial valves in patients with a small aortic annulus (≤ 21 mm) and evaluates the feasibility and safety of AVR in this population ...
Yu Sun +6 more
doaj +2 more sources
The criticality of reversible quadratic centers at the outer boundary of its period annulus
Journal of Differential Equations, 2022 This paper deals with the period function of the reversible quadratic centers where . Compactifying the vector field to , the boundary of the period annulus has two connected components, the center itself and a polycycle. We call them the inner and outer boundary of the period annulus, respectively.
Jordi Villadelprat, Marin David
exaly +7 more sources
The cyclicity of the period annulus of a reversible quadratic system [PDF]
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2021 We prove that perturbing the periodic annulus of the reversible quadratic polynomial differential system $\dot x=y+ax^2$, $\dot y=-x$ with a ≠ 0 inside the class of all quadratic polynomial differential systems we can obtain at most two limit cycles, including their multiplicities.
Liu, Changjian +2 more
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On the maximum number of period annuli for second order conservative equations
Mathematical Modelling and Analysis, 2021 We consider a second order scalar conservative differential equation whose potential function is a Morse function with a finite number of critical points and is unbounded at infinity.
Armands Gritsans, Inara Yermachenko
doaj +1 more source
Dynamics of annulus maps II: Periodic points for coverings [PDF]
Fundamenta Mathematicae, 2016 Summary: Let \(f\) be a covering map of the open annulus \(A= S^1\times (0,1)\) of degree \(d\), \(|d| > 1\). Assume that \(f\) preserves an essential (i.e not contained in a disk of \(A\)) compact subset \(K\). We show that \(f\) has at least the same number of periodic points in each period as the map \(z^d\) on \(S^1.\)
Iglesias, Jorge +3 more
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Action and periodic orbits on annulus
, 2021 14 ...
Deng, Yanxia, Xia, Zhihong
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New Model for the Assessment of Transcatheter Aortic Valve Replacement Devices in Sheep
Journal of Investigative Surgery, 2022 Background Transcatheter aortic valve replacement (TAVR) is an effective therapy in treating high-risk patients suffering from aortic stenosis. Animal models used to evaluate safety and efficacy of TAVR devices prior to clinical use lack a stenotic ...
John P. Carney +6 more
doaj +1 more source