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Phase portrait in conversation processes

2006
Our goal was to extract information on communicative process evolution avoiding simplification and classification. We analysed 50 motivational research interview made from students during their university course. The nature intrinsically interactive of the dialogue concretises, shapes and evolves within time dimension.
G Morgavi, V Florini
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Phase Portrait of CDS

1991
At the present time, it is apparently difficult to give a general and exhaustive definition of the phase portait of CDSs considered here. At the present stage of development of the theory, it can be adequately done for a second-order CDS defined on the plane or on a two- dimensional manifold (Sec. 34).
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Bifurcations of Phase Portraits

2000
The situation that we shall be concerned with in this chapter is the following: we consider a differential system that depends on auxiliary parameters (as in Chapt. 5, we may talk about control parameters, hidden parameters, imperfection parameters, … ) and we wish to understand how the phase portrait changes as the parameters vary.
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Stroboscopic phase portrait and strange attractors

Physics Letters A, 1978
Abstract External periodic modulation of a nonlinear oscillator may lead to a chaotic output behaviour. This phenomenon is attributed to the existence of a strange attractor, which embodies essentially a folding motion as is met in Bernoulli shift or the Baker's transformation.
Kazuhisa Tomita, Tohru Kai
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The phase plane portrait

1983
Since frequency response techniques and root locus diagrams are not applicable to a nonlinear process, there is an important need for a graphical tool to allow nonlinear behaviour to be displayed. This need is filled by the phase plane diagram. The method is applicable to second-order processes without input, although effects equivalent to step or ramp
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Phase Portraits of the Proliferation-Quiescence Decision

Science Signaling, 2013
The ON-OFF status of the CDK2-RB bistable switch, rather than a particular time point, defines the restriction point.
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Phase Portrait of the Matrix Riccati Equation

SIAM Journal on Control and Optimization, 1986
The matrix Riccati equations \(dK/dt=B_{21}+B_{22}K-KB_{11}- KB_{12}K\) (where \(K=K(t)\in {\mathbb{R}}^{m\times n}\) is variable and \(B_{12}\in {\mathbb{R}}^{m\times n}\), \(B_{22}\in {\mathbb{R}}^{m\times m}\), \(B_{11}\in {\mathbb{R}}^{n\times n}\), \(B_{12}\in {\mathbb{R}}^{n\times m}\) are constant matrices) and \(dK/dt=-Q-A'K-KA+KLK\) (where \(K=
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Analyzing oriented textures through phase portraits

[1990] Proceedings. 10th International Conference on Pattern Recognition, 2002
An attempt is made to develop a solution for signal-to-symbol transformation in the domain of flowlike or oriented texture. The geometric theory of differential equations is used to derive a symbol set based on the visual appearance of phase portraits. This theory provides a technique for describing textures both qualitatively and quantitatively.
A.R. Rao, R. Jain
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Economy Phase Portraits

1976
Topological terms like attractors and basins are expected to play an ever increasing role in the qualitative description of systems described by differential equations. This paper illustrates those concepts through a detailed study of the phase portraits of various "economic models" treated in the Energy Program of IIASA.
Grümm, H.-R., Schrattenholzer, L.
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Phase Portraits of Quadratic Systems

1997
As in the lecture given at the Conference, this paper intends to give an impression of what has become known so far about the phase portraits of quadratic systems in the plane. By a quadratic system is understood the system of two autonomous differential equations in the plane, where = and P(x, y) and Q(x, y) are relative prime polynomials, which are ...
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