Phase‐Plane Analysis of Nonlinear, Second‐Order, Ordinary Differential Equations

1971 ◽  
Vol 12 (7) ◽  
pp. 1339-1348 ◽  
Author(s):  
Lawrence Dresner
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Phase Plane ◽  
Second Order ◽  
Phase Plane Analysis ◽  
Plane Analysis

Phase Plane Analysis of Limb Trajectories in Nonhandicapped and Cerebral Palsied Subjects

1985 ◽  
Vol 2 (3) ◽  
pp. 214-227 ◽  
Author(s):  
Anne Beuter ◽  
Alan Garfinkel
Keyword(s):  
Dynamical System ◽  
Knee Joint ◽  
Phase Plane ◽  
Second Order ◽  
Study Phase ◽  
Phase Plane Analysis ◽  
Joint Angles ◽  
Kinematic Data ◽  
Movement Data ◽  
Plane Analysis

In this study, phase plane analysis was used to describe the mechanisms involved in human intralimb dynamics during a multijoint coordinated task. Nonhandicapped, spastic, and athetoid cerebral palsied individuals were videotaped as they performed a stepping task. Kinematic data for the hip and knee joint angles were digitized, smoothed, differentiated, and plotted. Phase plane analysis of movement data reveals striking differences between nonhandicapped and cerebral palsied individuals. Whereas nonhandicapped individuals have trajectories in the phase plane that suggest a self-contained second-order dynamical system, cerebral palsied individuals have self-interesting loops in their phase planes. Based upon these patterns some dynamical distinctions are offered, and suggestions are made toward a possible model.

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.

scholarly journals On Truly Nonlinear Oscillator Equations of Ermakov-Pinney Type

2021 ◽  
Vol 19 (6) ◽  
pp. 970-983
Author(s):  
Marcellin Nonti ◽  
Kolawole Kegnide Damien Adjai ◽  
Jean Akande ◽  
Marc Delphin Monsia
Keyword(s):  
Differential Equations ◽  
Phase Plane ◽  
Elliptic Functions ◽  
Nonlinear Oscillators ◽  
Phase Plane Analysis ◽  
Exact Integration ◽  
Plane Analysis ◽  
Existence Of Periodic Solutions ◽  
First Time ◽  
Oscillator Equations

In this paper we present a general class of differential equations of Ermakov-Pinney type which may serve as truly nonlinear oscillators. We show the existence of periodic solutions by exact integration after the phase plane analysis. The related quadratic Lienard type equations are examined to show for the first time that the Jacobi elliptic functions may be solution of second-order autonomous non-polynomial differential equations.

Phase plane analysis of second-order nonlinear differential-difference equations

1968 ◽  
Vol 13 (2) ◽  
pp. 200-201 ◽  
Author(s):  
W. Robinson ◽  
A. Soudack
Keyword(s):  
Difference Equations ◽  
Phase Plane ◽  
Second Order ◽  
Phase Plane Analysis ◽  
Plane Analysis

Phase-Plane Analysis of Solutions of the Helmholtz Equation for Electromagnetic Waves in Media with Self-Action

2020 ◽  
Vol 55 (4) ◽  
pp. 299-305
Author(s):  
H. V. Baghdasaryan ◽  
V. A. Vardanyan ◽  
A. V. Daryan
Keyword(s):  
Helmholtz Equation ◽  
Electromagnetic Waves ◽  
Phase Plane ◽  
Phase Plane Analysis ◽  
Plane Analysis
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