scholarly journals Global‐phase portrait and large‐degree asymptotics for the Kissing polynomials

2021 ◽  
Author(s):  
A. Barhoumi ◽  
A. F. Celsus ◽  
A. Deaño
Keyword(s):  
Phase Portrait ◽  
Large Degree ◽  
Global Phase Portrait

scholarly journals Global Phase Portrait and Bifurcation Diagram for a Multi-Parametric Linear System

2020 ◽  
Vol 55 (4) ◽  
Author(s):  
Jorge Rodríguez Contreras ◽  
Alberto Reyes Linero ◽  
Juliana Vargas Sánchez
Keyword(s):  
Linear System ◽  
Critical Point ◽  
Phase Portrait ◽  
Bifurcation Diagram ◽  
Critical Points ◽  
Global Dynamics ◽  
Parametric Surfaces ◽  
Critical Points At Infinity ◽  
Global Phase Portrait ◽  
The Stability

The goal of this article is to conduct a global dynamics study of a linear multiparameter system (real parameters (a,b,c) in R^3); for this, we take the different changes that these parameters present. First, we find the different parametric surfaces in which the space is divided, where the stability of the critical point is defined; we then create a bifurcation diagram to classify the different bifurcations that appear in the system. Finally, we determine and classify the critical points at infinity, considering the canonical shape of the Poincaré sphere, and thus, obtain a global phase portrait of the multiparametric linear system.

STRUCTURALLY STABLE TWO-CELL CELLULAR NEURAL NETWORKS

2004 ◽  
Vol 14 (08) ◽  
pp. 2579-2653 ◽  
Author(s):  
MAKOTO ITOH ◽  
LEON O. CHUA
Keyword(s):  
Neural Networks ◽  
Phase Portrait ◽  
Limit Cycles ◽  
Equilibrium Points ◽  
Cellular Neural Networks ◽  
Global Phase Portrait ◽  
Structurally Stable

The global phase portrait of structurally stable two-cell cellular neural networks is studied. The configuration of equilibrium points, the number of limit cycles and their locations are investigated systematically.

scholarly journals Bifurcations of the Riccati Quadratic Polynomial Differential Systems

2021 ◽  
Vol 31 (06) ◽  
pp. 2150094
Author(s):  
Jaume Llibre ◽  
Bruno D. Lopes ◽  
Paulo R. da Silva
Keyword(s):  
Phase Portrait ◽  
Differential System ◽  
Quadratic Polynomial ◽  
Phase Portraits ◽  
Topological Equivalence ◽  
Differential Systems ◽  
Polynomial Differential Systems ◽  
Polynomial Differential System ◽  
Global Phase Portrait ◽  
Poincaré Disk

In this paper, we characterize the global phase portrait of the Riccati quadratic polynomial differential system [Formula: see text] with [Formula: see text], [Formula: see text] nonzero (otherwise the system is a Bernoulli differential system), [Formula: see text] (otherwise the system is a Liénard differential system), [Formula: see text] a polynomial of degree at most [Formula: see text], [Formula: see text] and [Formula: see text] polynomials of degree at most 2, and the maximum of the degrees of [Formula: see text] and [Formula: see text] is 2. We give the complete description of the phase portraits in the Poincaré disk (i.e. in the compactification of [Formula: see text] adding the circle [Formula: see text] of the infinity) modulo topological equivalence.

scholarly journals Global phase portrait of a degenerate Bogdanov-Takens system with symmetry

2017 ◽  
Vol 22 (4) ◽  
pp. 1273-1293 ◽  
Author(s):  
Hebai Chen ◽  
◽  
Xingwu Chen ◽  
Jianhua Xie ◽  
◽  
...  
Keyword(s):  
Phase Portrait ◽  
Global Phase Portrait

GLOBAL DYNAMICS OF THE LORENZ SYSTEM WITH INVARIANT ALGEBRAIC SURFACES

2010 ◽  
Vol 20 (10) ◽  
pp. 3137-3155 ◽  
Author(s):  
JAUME LLIBRE ◽  
MARCELO MESSIAS ◽  
PAULO RICARDO DA SILVA
Keyword(s):  
Phase Portrait ◽  
Lorenz System ◽  
Algebraic Surfaces ◽  
Global Dynamics ◽  
State Variables ◽  
Poincaré Compactification ◽  
Invariant Algebraic Surfaces ◽  
The Lorenz System ◽  
Global Phase Portrait ◽  
Parameter Values

In this paper by using the Poincaré compactification of ℝ3 we describe the global dynamics of the Lorenz system [Formula: see text] having some invariant algebraic surfaces. Of course (x, y, z) ∈ ℝ3 are the state variables and (s, r, b) ∈ ℝ3 are the parameters. For six sets of the parameter values, the Lorenz system has invariant algebraic surfaces. For these six sets, we provide the global phase portrait of the system in the Poincaré ball (i.e. in the compactification of ℝ3 with the sphere 𝕊2 of the infinity).

Local and global phase portrait of equation $\dot z=f(z)$

2007 ◽  
Vol 17 (2) ◽  
pp. 309-329 ◽  
Author(s):  
Antonio Garijo ◽  
◽  
Armengol Gasull ◽  
Xavier Jarque ◽  
◽  
...  
Keyword(s):  
Phase Portrait ◽  
Global Phase Portrait

Characterization of homoepitaxial diamond films by Electron microscopy

1991 ◽  
Vol 49 ◽  
pp. 880-881
Author(s):  
D.P. Malta ◽  
S.A. Willard ◽  
R.A. Rudder ◽  
G.C. Hudson ◽  
J.B. Posthill ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Surface Defects ◽  
Substrate Surface ◽  
Diamond Films ◽  
Chemical Vapor ◽  
Polycrystalline Diamond ◽  
Large Degree ◽  
Rf Plasma ◽  
Semiconducting Diamond

Semiconducting diamond films have the potential for use as a material in which to build active electronic devices capable of operating at high temperatures or in high radiation environments. A major goal of current device-related diamond research is to achieve a high quality epitaxial film on an inexpensive, readily available, non-native substrate. One step in the process of achieving this goal is understanding the nucleation and growth processes of diamond films on diamond substrates. Electron microscopy has already proven invaluable for assessing polycrystalline diamond films grown on nonnative surfaces.The quality of the grown diamond film depends on several factors, one of which is the quality of the diamond substrate. Substrates commercially available today have often been found to have scratched surfaces resulting from the polishing process (Fig. 1a). Electron beam-induced current (EBIC) imaging shows that electrically active sub-surface defects can be present to a large degree (Fig. 1c). Growth of homoepitaxial diamond films by rf plasma-enhanced chemical vapor deposition (PECVD) has been found to planarize the scratched substrate surface (Fig. 1b).

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