Asymptotics beyond All Orders for a Certain Type of Nonlinear Oscillators

1996 ◽  
Vol 96 (1) ◽  
pp. 85-109 ◽  
Author(s):  
Jishan Hu
Keyword(s):  
Nonlinear Oscillators ◽  
Asymptotics Beyond All Orders

Performance analysis of global local mean square error criterion of stochastic linearization for nonlinear oscillator

2019 ◽  
Author(s):  
Nguyen Cao Thang ◽  
Luu Xuan Hung
Keyword(s):  
Performance Analysis ◽  
Mean Square Error ◽  
Nonlinear Oscillators ◽  
Degree Of Freedom ◽  
Equivalent Linearization ◽  
Mean Square ◽  
Error Criterion ◽  
Stochastic Linearization ◽  
Local Mean ◽  
Mean Square Error Criterion

The paper presents a performance analysis of global-local mean square error criterion of stochastic linearization for some nonlinear oscillators. This criterion of stochastic linearization for nonlinear oscillators bases on dual conception to the local mean square error criterion (LOMSEC). The algorithm is generally built to multi degree of freedom (MDOF) nonlinear oscillators. Then, the performance analysis is carried out for two applications which comprise a rolling ship oscillation and two degree of freedom one. The improvement on accuracy of the proposed criterion has been shown in comparison with the conventional Gaussian equivalent linearization (GEL).

A new modification of the homotopy perturbation method

2021 ◽  
pp. 095745652199987
Author(s):  
Magaji Yunbunga Adamu ◽  
Peter Ogenyi
Keyword(s):  
Comparative Analysis ◽  
Error Analysis ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Oscillators ◽  
Absolute Error ◽  
New Method ◽  
Optimal Analysis ◽  
Homotopy Perturbation ◽  
Accuracy And Precision

This study proposes a new modification of the homotopy perturbation method. A new parameter alpha is introduced into the homotopy equation in order to improve the results and accuracy. An optimal analysis identifies the parameter alpha, aimed at improving the solutions. A comparative analysis of the proposed method reveals that the new method presents results with higher degree of accuracy and precision than the classic homotopy perturbation method. Absolute error analysis shows the convenience of the proposed method, providing much smaller errors. Two examples are presented: Duffing and Van der pol’s nonlinear oscillators to demonstrate the efficiency, accuracy, and applicability of the new method.

scholarly journals Reconstructing the structure of directed and weighted networks of nonlinear oscillators

2017 ◽  
Vol 95 (4) ◽  
Author(s):  
Francesco Alderisio ◽  
Gianfranco Fiore ◽  
Mario di Bernardo
Keyword(s):  
Nonlinear Oscillators ◽  
Weighted Networks

Nonlinear Resonance in Neuron Dynamics

1995 ◽  
Vol 50 (8) ◽  
pp. 718-726 ◽  
Author(s):  
Scott Rader ◽  
Diek W. Wheeler ◽  
W.C. Schieve ◽  
Pranab Das
Keyword(s):  
Neural Networks ◽  
Energy Transfer ◽  
Power Spectrum ◽  
Nonlinear Resonance ◽  
Nonlinear Oscillators ◽  
Hopfield Neural Networks ◽  
Neuron Dynamics

Abstract Hübler's technique using aperiodic forces to drive nonlinear oscillators to resonance is analyzed. The oscillators being examined are effective neurons that model Hopfield neural networks. The method is shown to be valid under several different circumstances. It is verified through analysis of the power spectrum, force, resonance, and energy transfer of the system.

scholarly journals Oscillation death in coupled counter-rotating identical nonlinear oscillators

2019 ◽  
Vol 100 (2) ◽  
Author(s):  
Jung-Wan Ryu ◽  
Woo-Sik Son ◽  
Dong-Uk Hwang
Keyword(s):  
Nonlinear Oscillators

scholarly journals Experimental Observation of the Amplitude Death Effect in Two Coupled Nonlinear Oscillators

2000 ◽  
Vol 84 (23) ◽  
pp. 5312-5315 ◽  
Author(s):  
R. Herrero ◽  
M. Figueras ◽  
J. Rius ◽  
F. Pi ◽  
G. Orriols
Keyword(s):  
Experimental Observation ◽  
Nonlinear Oscillators ◽  
Amplitude Death ◽  
Coupled Nonlinear Oscillators

Synchronized Periodic Solutions of a Class of Periodically Driven Nonlinear Oscillators

1988 ◽  
Vol 55 (3) ◽  
pp. 721-728 ◽  
Author(s):  
Gamal M. Mahmoud ◽  
Tassos Bountis
Keyword(s):  
Periodic Solutions ◽  
Periodic Orbits ◽  
Nonlinear Oscillators ◽  
High Energy ◽  
Second Order ◽  
Multiple Time ◽  
Particle Beams ◽  
Periodically Driven ◽  
Time Scaling ◽  
A New Technique

We consider a class of parametrically driven nonlinear oscillators: x¨ + k1x + k2f(x,x˙)P(Ωt) = 0, P(Ωt + 2π) = P(Ωt)(*) which can be used to describe, e.g., a pendulum with vibrating length, or the displacements of colliding particle beams in high energy accelerators. Here we study numerically and analytically the subharmonic periodic solutions of (*), with frequency 1/m ≅ √k1, m = 1, 2, 3,…. In the cases of f(x,x˙) = x3 and f(x,x˙) = x4, with P(Ωt) = cost, all of these so called synchronized periodic orbits are obtained numerically, by a new technique, which we refer to here as the indicatrix method. The theory of generalized averaging is then applied to derive highly accurate expressions for these orbits, valid to the second order in k2. Finally, these analytical results are used, together with the perturbation methods of multiple time scaling, to obtain second order expressions for regions of instability of synchronized periodic orbits in the k1, k2 plane, which agree very well with the results of numerical experiments.

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