scholarly journals Global phase- portrait of a plane autonomous system

1964 ◽  
Vol 14 (1) ◽  
pp. 87-97 ◽  
Author(s):  
Czeslaw Olech
Keyword(s):  
Phase Portrait ◽  
Autonomous System ◽  
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).

scholarly journals Generalized model of interacting dark energy and dark matter: Phase portrait analysis for evolving universe

2022 ◽  
Author(s):  
Giridhari Deogharia ◽  
Mayukh Bandyopadhyay ◽  
Ritabrata Biswas
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Cosmological Model ◽  
Phase Portrait ◽  
Critical Points ◽  
Autonomous System ◽  
Cosmic Acceleration ◽  
Accelerating Universe ◽  
Late Time ◽  
Phase Portrait Analysis

The main aim of this work is to give a suitable explanation of present accelerating universe through an acceptable interactive dynamical cosmological model. A three-fluid cosmological model is introduced in the background of Friedmann–Lemaître–Robertson-Walker asymptotically flat spacetime. This model consists of interactive dark matter and dark energy with baryonic matter, taken as perfect fluid, satisfying barotropic equation of state. We consider dust as the candidate of dark matter. A scalar field [Formula: see text] represents dark energy with potential [Formula: see text]. Einstein’s field equations are utilized to construct a three-dimensional interactive autonomous system by choosing suitable interaction between dark energy and dark matter. We take the interaction kernel as [Formula: see text], where [Formula: see text] indicates the density of dark energy, [Formula: see text] is the interacting constant and [Formula: see text] is Hubble parameter. In order to explain the stability of this system, we obtain some suitable critical points. We analyze stability of obtained critical points to show the different phases of universe and cosmological implications. Surprisingly, we find some stable critical points which represent late-time dark energy-dominated era when a model parameter [Formula: see text] is equal to [Formula: see text]. We introduce a two-dimensional interactive autonomous system and after phase portrait analysis of it, we get several stable points which represent dark energy-dominated era and late-time cosmic acceleration simultaneously. Here, we also demonstrate the variation in interaction at vicinity of phantom barrier [Formula: see text]. From our work, we can also predict the future phase evolution of the universe.

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
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