Results 241 to 250 of about 6,937,403 (296)

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 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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Phase Portraits of the Discontinuous Planar Piecewise Linear Differential Systems of Focus-Center Type

Qualitative Theory of Dynamical Systems, 2022
Lizhong Xiong, Kuilin Wu, Shimin Li
semanticscholar   +1 more source

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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Global phase portraits of planar piecewise linear refracting systems of saddle–saddle type

, 2021
Yi-Shi Shao, Shimin Li, Kuilin Wu
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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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'Phase portraits' for characterizing advanced lasers

Optical Fiber Communication Conference. Technical Digest Postconference Edition. Trends in Optics and Photonics Vol.37 (IEEE Cat. No. 00CH37079), 2002
We show that plotting the instantaneous optical frequency against power gives an instantly recognizable and useful fingerprint of the dynamic operation of lasers. We show simulated examples of bulk, MQW, unstable and tunable lasers.
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Invariant conditions for phase portraits of quadratic systems with complex conjugate invariant lines meeting at a finite point

Rendiconti del Circolo Matematico di Palermo Series 2, 2020
Joan C. Artés, J. Llibre, D. Schlomiuk, N. Vulpe   +3 more
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