scholarly journals Diagnosis of a ferroresonance type through visualisation

2019 ◽  
Vol 28 ◽  
pp. 01039
Author(s):  
Łukasz Majka ◽  
Maciej Klimas
Keyword(s):  
Differential Equations ◽  
Phase Plane ◽  
Nonlinear Differential Equations ◽  
Visual Display ◽  
Time Dependent ◽  
Poincaré Maps ◽  
Poincare Maps ◽  
Test Circuit ◽  
Plane Space ◽  
Time Dependent System

The paper is focused on presenting the possible enhancements in visualisation of the ferroresonance phenomenon. The investigations have been performed with the usage of overcurrent/overvoltage responses of a ferroresonance circuit. The waveforms have been measured and recorded in a ferroresonant test circuit. Phase–plane/–space graphs analysed in this paper are a visual display of certain type characteristics for the time dependent system of nonlinear differential equations. The application of Poincare maps is also mentioned in the paper.

Observation and Evolution of Chaos for an Autonomous System

1984 ◽  
Vol 51 (3) ◽  
pp. 664-673 ◽  
Author(s):  
E. H. Dowell
Keyword(s):  
Elastic Plate ◽  
Physical Interpretation ◽  
Autonomous System ◽  
Phase Plane ◽  
Power Spectra ◽  
Poincaré Maps ◽  
Flowing Fluid ◽  
Poincare Maps ◽  
Time Histories

Time histories, phase plane portraits, power spectra, and Poincare maps are used as descriptors to observe the evolution of chaos in an autonomous system. Although the motions of such a system can be quite complex, these descriptors prove helpful in detecting the essential structure of the motion. Here the principal interest is in phase plane portraits and Poincare maps, their methods of construction, and physical interpretation. The system chosen for study has been previously discussed in the literature, i.e., the flutter of a buckled elastic plate in a flowing fluid.

Limit cycle analysis of the verge and foliot clock escapement using impulsive differential equations and Poincaré maps

2003 ◽  
Vol 76 (17) ◽  
pp. 1685-1698 ◽  
Author(s):  
Alexander V. Roup ◽  
Dennis S. Bernstein ◽  
Sergey G. Nersesov ◽  
Wassim M. Haddad ◽  
VijaySekhar Chellaboina
Keyword(s):  
Differential Equations ◽  
Limit Cycle ◽  
Impulsive Differential Equations ◽  
Poincaré Maps ◽  
Poincare Maps

Simplicial approximation of Poincaré maps of differential equations

1987 ◽  
Vol 124 (1-2) ◽  
pp. 59-64 ◽  
Author(s):  
Frank Varosi ◽  
Celso Grebogi ◽  
James A Yorke
Keyword(s):  
Differential Equations ◽  
Poincaré Maps ◽  
Simplicial Approximation ◽  
Poincare Maps

A non-oscillation theorem for nonlinear differential equations with p-Laplacian

2006 ◽  
Vol 136 (3) ◽  
pp. 633-647 ◽  
Author(s):  
Jitsuro Sugie ◽  
Masakazu Onitsuka
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Linear Differential Equation ◽  
Phase Plane ◽  
Nonlinear Differential Equations ◽  
Phase Plane Analysis ◽  
Oscillation Theorem ◽  
Plane Analysis ◽  
Linear Differential

The equation considered in this paper is tp(φp(x′))′ + g(x) = 0, where φp(x′) = |x′|p−2x′ with p > 1, and g(x) satisfies the signum condition xg(x) > 0 if x ≠ 0 but is not assumed to be monotone. Our main objective is to establish a criterion on g(x) for all non-trivial solutions to be non-oscillatory. The criterion is the best possible. The method used here is the phase-plane analysis of a system equivalent to this differential equation. The asymptotic behaviour is also examined in detail for eventually positive solutions of a certain half-linear differential equation.

Presenting joint kinematics of human locomotion using phase plane portraits and Poincaré maps

1994 ◽  
Vol 27 (12) ◽  
pp. 1495-1499 ◽  
Author(s):  
Yildirim Hurmuzlu ◽  
Cagatay Basdogan ◽  
James J. Carollo
Keyword(s):  
Phase Plane ◽  
Human Locomotion ◽  
Joint Kinematics ◽  
Poincaré Maps ◽  
Poincare Maps

scholarly journals Specific Differential Equations for Generating Pulse Sequences

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
Ghiocel Toma
Keyword(s):  
Differential Equations ◽  
Pulse Sequence ◽  
Nonlinear Differential Equations ◽  
Pulse Sequences ◽  
Continuous Functions ◽  
Second Order ◽  
Time Dependent ◽  
Second Order Differential Equations ◽  
Null Values ◽  
Constant Slope

This study presents nonlinear differential equations capable to generate continuous functions similar to pulse sequences. First are studied some basic properties of second-order differential equations with time-dependent coefficients generating bounded oscillating functions similar to test-functions (the function and its derivative being equal to zero at the same time moments). The necessary intercorrelations between the phase of generated oscillations and the time-dependent coefficients is presented, being shown also that the external command function should be set to a constant value at these time moments so as to determine the amplitude and the sign of generated oscillations. Then some possibilities of using previous differential equation for generating positive-definite functions with null values for the function and its derivative at the same time moments and with constant slope for its amplitude are presented, being shown that the corresponding external command function should present also alternating components. Finally all previous results are used for determining a set of second-order differential equations with time dependent coefficients and a set of external command and corrective functions for generating a pulse sequence useful for modelling time series.

Dynamics of a Pumping System

2016 ◽  
Vol 823 ◽  
pp. 85-90
Author(s):  
Nicolae Dumitru ◽  
Dan B. Marghitu ◽  
Nicolae Craciunoiu
Keyword(s):  
Angular Velocity ◽  
Dynamic Stability ◽  
Lyapunov Exponents ◽  
Chaotic Motion ◽  
Phase Plane ◽  
Elastic Displacement ◽  
Poincaré Maps ◽  
Poincare Maps ◽  
Pumping System ◽  
Largest Lyapunov Exponents

In this paper a pumping systems for deep extraction is simulated using SolidWorks and ADAMS. The elastic displacement of a point on the flexible moving cable is analyzed. The dynamics of the system is characterized with phase plane, Poincaré maps, and Lyapunov exponents. The Lyapunovexponents represent the dynamic stability of the system. The largest Lyapunov exponents for three different angular velocity show the chaotic motion of the system

A Computer-Simulated Method of Phase-Plane Displacements

1970 ◽  
Vol 92 (2) ◽  
pp. 233-237 ◽  
Author(s):  
Louis L. Scharf
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Phase Plane ◽  
Nonlinear Differential Equations ◽  
Variable Coefficients ◽  
Time Variable ◽  
Second Order Differential Equations ◽  
Simple Set ◽  
Linear And Nonlinear ◽  
Plane Technique

A well-known graphical phase-plane technique for solving a wide variety of ordinary second-order differential equations is shown to satisfy a relatively simple set of iterative relationships which are easily programmed on a digital computer. The only restriction on the differential equation of interest is that it can be written as ax¨ + G(x, x˙, t) = 0, where G(x, x˙, t) = g(x, x˙, t) + kx. Consequently, many linear and nonlinear differential equations, with or without forcing functions, which may also have (explicit) time-variable coefficients, are easily solved with the method.

Sign in / Sign up

Export Citation Format

Share Document