Continuous Media: Interpretation in Terms of Phase-Portrait Method for Dynamic Systems with Control

The phase portrait of the second and higher order differential equations presents in graphical form the behavior of the solution set without solving the equation. In this way, the stability of a dynamic system and its long-time behavior can be studied. The article explores the capabilities of Mathcad for analysis of systems by the phase plane method. A sequence of actions using Mathcad's operators to build phase portrait and phase trace analysis is proposed. An example is given by a differential equation of the second order. The approach is also applicable to systems of higher order.

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Phase Shadows: An Enhanced Representation of Nonlinear Dynamic Systems

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127417300518 ◽

2017 ◽

Vol 27 (14) ◽

pp. 1730051

Author(s):

Amalia Luque ◽

Julio Barbancho ◽

Javier Fernández Cañete ◽

Antonio Córdoba

Keyword(s):

Phase Portrait ◽

Dynamic Systems ◽

Limit Cycles ◽

Nonlinear Dynamic ◽

Equilibrium Points ◽

Nonlinear Dynamic Systems ◽

Phase Portraits ◽

Chaotic Attractors ◽

System Behavior ◽

Cylindrical Phase

Many nonlinear dynamic systems have a rotating behavior where an angle defining its state may extend to more than 360[Formula: see text]. In these cases the use of the phase portrait does not properly depict the system’s evolution. Normalized phase portraits or cylindrical phase portraits have been extensively used to overcome the original phase portrait’s disadvantages. In this research a new graphic representation is introduced: the phase shadow. Its use clearly reveals the system behavior while overcoming the drawback of the existing plots. Through the paper the method to obtain the graphic is stated. Additionally, to show the phase shadow’s expressiveness, a rotating pendulum is considered. The work exposes that the new graph is an enhanced representational tool for systems having equilibrium points, limit cycles, chaotic attractors and/or bifurcations.

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On the phase portrait of a class of large nonlinear dynamic systems such as the power system

IEEE Transactions on Automatic Control ◽

10.1109/9.356 ◽

1988 ◽

Vol 33 (1) ◽

pp. 4-15 ◽

Cited By ~ 115

Author(s):

J. Zaborszky ◽

G. Huang ◽

B. Zheng ◽

T.-C. Leung

Keyword(s):

Power System ◽

Phase Portrait ◽

Dynamic Systems ◽

Nonlinear Dynamic ◽

Nonlinear Dynamic Systems

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Phase behavior of cationic and anionic surfactants at low concentrations

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100123878 ◽

1992 ◽

Vol 50 (1) ◽

pp. 694-695

Author(s):

E. Naranjo

Keyword(s):

Phase Behavior ◽

Structural Characterization ◽

Dynamic Systems ◽

Anionic Surfactants ◽

Intermolecular Forces ◽

Stable Form ◽

Surfactant Mixtures ◽

Low Concentrations ◽

Cationic And Anionic Surfactants ◽

General Method

Equilibrium vesicles, those which are the stable form of aggregation and form spontaneously on mixing surfactant with water, have never been demonstrated in single component bilayers and only rarely in lipid or surfactant mixtures. Designing a simple and general method for producing spontaneous and stable vesicles depends on a better understanding of the thermodynamics of aggregation, the interplay of intermolecular forces in surfactants, and an efficient way of doing structural characterization in dynamic systems.

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Improving Feeding Outcomes in the NICU: Moving From Volume-Driven to Infant-Driven Feeding

Perspectives on Swallowing and Swallowing Disorders (Dysphagia) ◽

10.1044/sasd19.3.68 ◽

2010 ◽

Vol 19 (3) ◽

pp. 68-74 ◽

Cited By ~ 9

Author(s):

Catherine S. Shaker

Keyword(s):

Intensive Care Unit ◽

Dynamic Systems ◽

Neonatal Intensive Care ◽

Well Being ◽

Dynamic Systems Theory ◽

Feeding Problems ◽

Care Giving ◽

Extremely Preterm ◽

Extremely Preterm Infants

Current research on feeding outcomes after discharge from the neonatal intensive care unit (NICU) suggests a need to critically look at the early underpinnings of persistent feeding problems in extremely preterm infants. Concepts of dynamic systems theory and sensitive care-giving are used to describe the specialized needs of this fragile population related to the emergence of safe and successful feeding and swallowing. Focusing on the infant as a co-regulatory partner and embracing a framework of an infant-driven, versus volume-driven, feeding approach are highlighted as best supporting the preterm infant's developmental strivings and long-term well-being.

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A Dynamic Systems Approach to Personality

European Psychologist ◽

10.1027//1016-9040.6.3.172 ◽

2001 ◽

Vol 6 (3) ◽

pp. 172-176 ◽

Cited By ~ 14

Author(s):

Lawrence A. Pervin

Keyword(s):

Dynamic Systems ◽

Systems Approach ◽

Biological Processes ◽

Recent Advances ◽

Dynamic View ◽

The Future ◽

History Of

David Magnusson has been the most articulate spokesperson for a holistic, systems approach to personality. This paper considers three concepts relevant to a dynamic systems approach to personality: dynamics, systems, and levels. Some of the history of a dynamic view is traced, leading to an emphasis on the need for stressing the interplay among goals. Concepts such as multidetermination, equipotentiality, and equifinality are shown to be important aspects of a systems approach. Finally, attention is drawn to the question of levels of description, analysis, and explanation in a theory of personality. The importance of the issue is emphasized in relation to recent advances in our understanding of biological processes. Integrating such advances into a theory of personality while avoiding the danger of reductionism is a challenge for the future.

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