Results 11 to 20 of about 436 (168)
Normal Form Analysis of Hopf Bifurcation Exemplified by Duffing’s Equation
Shock and Vibration, 1994 A method is proposed for calculating the normal form coefficients of the degenerate Hopf bifurcation system and the steady periodic solutions of a nonlinear vibration system.
A.Y.T. Leung, Zhang Qichang, Chen Yushu
doaj +1 more source
Stability analysis of embedded nonlinear predictor neural generalized predictive controller
Alexandria Engineering Journal, 2014 Nonlinear Predictor-Neural Generalized Predictive Controller (NGPC) is one of the most advanced control techniques that are used with severe nonlinear processes. In this paper, a hybrid solution from NGPC and Internal Model Principle (IMP) is implemented
Hesham F. Abdel Ghaffar +2 more
doaj +1 more source
On multivalued Duffing equation
Journal of Mathematical Analysis and Applications, 2018 The authors consider boundary value problems for a Duffing-type differential equation with multivalued terms. Two problems are investigated: The first problem is to find \(x \in W^{2,1}\bigl((0,1)\bigr) \cap H^1_0\bigl((0,1)\bigr)\) such that \[ -x'' - r(t)x' + N_1(t,x) \ni f(t) \quad \text{a.e.
Piotr Kalita, Piotr M. Kowalski
openaire +2 more sources
Background: On Georg Duffing and the Duffing Equation
, 2022 In this chapter a historical background to Duffing's work is given. In addition, his biography and bibliography are presented. The content of his famous book is described. The evolution of his work to the present day is also tracked. © 2011 John Wiley & Sons, Ltd. All rights reserved.
Kovacic, Ivana, Brennan, Michael J.
openaire +2 more sources
A GOOD INITIAL GUESS FOR APPROXIMATING NONLINEAR OSCILLATORS BY THE HOMOTOPY PERTURBATION METHOD [PDF]
, 2023 A good initial guess and an appropriate homotopy equation are two main factors in applications of the homotopy perturbation method. For a nonlinear oscillator, a cosine function is used in an initial guess.
Alsolami, Abdulrahman Ali +2 more
core +2 more sources
Comparisons between harmonic balance and nonlinear output frequency response function in nonlinear system analysis [PDF]
, 2008 By using the Duffing oscillator as a case study, this paper shows that the harmonic components in the nonlinear system response to a sinusoidal input calculated using the Nonlinear Output Frequency Response Functions (NOFRFs) are one of the solutions ...
Billings, S.A. +3 more
core +1 more source
Homotopy perturbation method with an auxiliary parameter for nonlinear oscillators
Journal of Low Frequency Noise, Vibration and Active Control, 2019 A brief introduction to the development of the homotopy perturbation method is given, and the main milestones are elucidated with more than 90 references.
Dan-Ni Yu, Ji-Huan He, Andres G Garcıa
doaj +1 more source
An algorithm for higher order Hopf normal forms [PDF]
, 1995 Normal form theory is important for studying the qualitative behavior of nonlinear oscillators. In some cases, higher order normal forms are required to understand the dynamic behavior near an equilibrium or a periodic orbit.
Ge, T, Leung, AYT
core +3 more sources
Approximate Solution of Nonlinear Oscillatory Circuits (II) [PDF]
, 1967 In the preceding paper a new method of analyzing nonlinear periodic oscillations was proposed. In this article a new conception, which is named as the extended harmonic approximation of nonlinear oscillatory circuits, is presented.
Baba, Yukinobu +3 more
core +1 more source
Autoresonance in a Dissipative System
, 2009 We study the autoresonant solution of Duffing's equation in the presence of dissipation. This solution is proved to be an attracting set. We evaluate the maximal amplitude of the autoresonant solution and the time of transition from autoresonant growth ...
Bogolyubov N N +14 more
core +1 more source