Stochastic potential for a periodically forced nonlinear oscillator

1998 ◽  
Vol 108 (5) ◽  
pp. 2088-2103 ◽  
Author(s):  
William Vance ◽  
John Ross
Keyword(s):  
Nonlinear Oscillator ◽  
Forced Nonlinear Oscillator

U-sequence and period-tripling phenomena in a forced nonlinear oscillator

1985 ◽  
Vol 2 (5) ◽  
pp. 213-216 ◽  
Author(s):  
Wu Shu-xian ◽  
Pei Liu-qing ◽  
Guo Fen
Keyword(s):  
Nonlinear Oscillator ◽  
Forced Nonlinear Oscillator

Forced nonlinear oscillator with nonsymmetric dry friction

2006 ◽  
Vol 77 (5) ◽  
pp. 353-362 ◽  
Author(s):  
K. Zimmermann ◽  
I. Zeidis ◽  
M. Pivovarov ◽  
K. Abaza
Keyword(s):  
Dry Friction ◽  
Nonlinear Oscillator ◽  
Forced Nonlinear Oscillator

scholarly journals Rotating vector solving method applied for nonlinear oscillator

2021 ◽  
Author(s):  
L. Cveticanin ◽  
P. Suchy ◽  
I. Biro ◽  
M. Zukovic
Keyword(s):  
Nonlinear Oscillator ◽  
Excitation Frequency ◽  
Elastic Beam ◽  
Degree Of Freedom ◽  
Linear Oscillator ◽  
Finite Degree ◽  
Vector Method ◽  
Three Degree Of Freedom ◽  
Excited Oscillator ◽  
Forced Nonlinear Oscillator

AbstractSignificant number of procedures for solving of the finite degree-of-freedom forced nonlinear oscillator are developed. For all of them it is common that they are based on the exact solution of the corresponding linear oscillator. For technical reasons, the aim of this paper is to develop a simpler solving procedure. The rotating vector method, developed for the linear oscillator, is adopted for solving of the nonlinear finite degree-of-freedom oscillator. The solution is assumed in the form of trigonometric functions. Assuming that the nonlinearity is small all terms of the series expansion of the function higher than the first are omitted. The rotating vectors for each mass are presented in the complex plane. In the paper, the suggested rotating vector procedure is applied for solving of a three-degree-of-freedom periodically excited oscillator. The influence of the nonlinear stiffness of the flexible elastic beam, excited with a periodical force, on the resonant properties of the system in whole is investigated. It is obtained that the influence of nonlinearity on the amplitude and phase of vibration is more significant for smaller values of the excitation frequency than for higher ones.

A theory for phase locking of respiration in cats to a mechanical ventilator

1984 ◽  
Vol 246 (3) ◽  
pp. R311-R320 ◽  
Author(s):  
G. A. Petrillo ◽  
L. Glass
Keyword(s):  
Nonlinear Oscillator ◽  
Phase Locking ◽  
Experimental Studies ◽  
Mechanical Ventilator ◽  
Van Der Pol Equation ◽  
Van Der Pol ◽  
Mechanically Ventilated ◽  
Wide Range ◽  
Forced Nonlinear Oscillator ◽  
Good Agreement

A mathematical model describing the Hering-Breuer reflexes in mechanically ventilated cats is developed. There is good agreement between the properties of the model and experimental studies performed over a wide range of frequencies and volumes of the mechanical ventilator. There is a correspondence between the model and a periodically forced nonlinear oscillator, similar to the van der Pol equation. Brain stem mechanisms underlying the entrainment are discussed.

On chaotic wave patterns in periodically forced steady-state KdVB and extended KdVB equations

2005 ◽  
Vol 461 (2061) ◽  
pp. 2857-2885 ◽  
Author(s):  
E.A Cox ◽  
M.P Mortell ◽  
A.V Pokrovskii ◽  
O Rasskazov
Keyword(s):  
Steady State ◽  
General Model ◽  
Nonlinear Oscillator ◽  
Classical Problem ◽  
Degree Theory ◽  
Viscous Damping ◽  
Topological Degree Theory ◽  
Nonlinear Anal ◽  
Wave Patterns ◽  
Forced Nonlinear Oscillator

The periodically forced KdVB and extended KdVB equations are considered. We investigate the structure of the totality of steady profiles. The existence of profiles that are close to any shuffling of two basic profiles is proved, and hence the existence of spatially chaotic and recurrent solutions. The proofs are based on topological degree theory to analyse chaotic behaviour. These proofs combine ideas suggested by P. Zgliczyński ( Zgliczyński 1996 Topol. Methods Nonlinear Anal . 8 , 169–177 ) with the method of topological shadowing. The results are also applicable to the classical problem of a quite general model of a forced nonlinear oscillator with viscous damping.

WAVELET ANALYSIS OF A NONLINEAR OSCILLATOR TRANSIENT DURING SYNCHRONIZATION

1996 ◽  
Vol 06 (12b) ◽  
pp. 2557-2570 ◽  
Author(s):  
H. FRANCO
Keyword(s):  
Simple Model ◽  
Nonlinear System ◽  
Wavelet Analysis ◽  
Spectral Line ◽  
Nonlinear Oscillator ◽  
Energy Exchange ◽  
Chaotic Phenomena ◽  
Transient Spectra ◽  
Forced Nonlinear Oscillator

A forced nonlinear oscillator can exhibit complex transient spectra even in the absence of chaotic phenomena. Series of evenly spaced lines appear in spectrograms of the numerically computed oscillations. They can be explained by means of a simple model describing the dynamics of the energy exchange between the external oscillating force and the nonlinear system. The resulting amplitude and phase modulations are shown to produce the spectral line structures. Frequencies incommensurable with other present frequencies can be generated by the nonlinear system.

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