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Bifurcations of Phase Portraits
2000The 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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Phase Portrait of the Matrix Riccati Equation
SIAM Journal on Control and Optimization, 1986The 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, 2002An 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. Ravishankar Rao, Ramesh C. Jain
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Phase portrait in conversation processes
2006Our 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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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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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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On the Phase Portrait Phase Portrait of the System $${{\dot x} = {Ax} + {\langle a, x\rangle x}}$$
Qualitative Theory of Dynamical Systems, 2012Structure of the phase space of the nonlinear system \({{\dot {\varvec x} = {\varvec Ax} + {\langle {\varvec a}, {\varvec x}\rangle {\varvec x}}}}\) is clarified using saddle-node bifurcations \({{{\varvec x}, {\varvec a} \in \mathbb{R}^d,}}\) is a d × d-matrix).
Abdulla Azamov, Dilmurod Boytillaev
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Quantifying complexity and variability in phase portraits of gait
Clinical Biomechanics, 2010Injuries to the lower extremity often cause limitations to joint motion and alter movement patterns of limb segments during gait. We hypothesized that complexity and variability of limb segment motion during gait would increase in both limbs due to unilateral injury.
Louis A, DiBerardino +4 more
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Nonlinear phase portrait modeling of fingerprint orientation
ICARCV 2004 8th Control, Automation, Robotics and Vision Conference, 2004., 2005Fingerprint orientation is crucial for automatic fingerprint identification. However, recovery of orientation is still difficult especially in noisy region. A way to aid recovery of the orientation is to provide an orientation model. In this paper, an orientation model for the entire fingerprint orientation using high order phase portrait is suggested.
Wei-Yun Yau, Jun Li 0005, Han Wang 0001
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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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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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Nonlinear phase portrait models for oriented textures
Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, 2002Nonlinear differential equations in Taylor series form are employed to model oriented textures. These models build upon the linear phase portrait description. Inclusion of higher order nonlinear terms provides a more accurate description in critical point regions.
Ralph M. Ford, Robin N. Strickland
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