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2011, 1. Aufl., ISBN 9780470977859, xvi, 369
The Duffing Equation: Nonlinear Oscillators and their Behaviourbrings together the results of a wealth of disseminated research literature on the Duffing equation, a key engineering model with a vast number... 
Duffing equations | Nonlinear oscillators | Mathematical models
Book
Journal of Sound and Vibration, ISSN 0022-460X, 03/2014, Volume 333, Issue 7, pp. 2040 - 2053
The probability structure of the response and energy harvested from a nonlinear oscillator subjected to white noise excitation is investigated by solution of the corresponding Fokker–Planck (FP) equation... 
ACOUSTICS | VIBRATIONS | MECHANICS | OPTIMIZATION | ENGINEERING, MECHANICAL | Monte Carlo method | Physicians (General practice) | Electric power production | Magnets, Permanent | Electric potential | Vibration | Computer simulation | Mathematical analysis | Voltage | Nonlinearity | Excitation | Filled plastics | Energy harvesting
Journal Article
Applied Mathematical Modelling, ISSN 0307-904X, 12/2015, Volume 39, Issue 23-24, pp. 7420 - 7426
We study a Wick-type stochastic reaction Duffing equation, and obtain some new exact solutions with the help of the white-noise theory and the exact solution of the Riccati equation... 
Wick-type stochastic reaction Duffing equation | Exact solutions | White-noise theory | Wick-type stochastic reaction Duffing | Equation | CHAOS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | EXP-FUNCTION METHOD | BIFURCATION
Journal Article
International journal of non-linear mechanics, ISSN 0020-7462, 10/2018, Volume 105, pp. 173 - 178
The nonlinear dynamics of action potentials in the FitzHugh–Nagumo model is addressed using a modified Van der Pol equation with fractional-order derivative and periodic parametric excitation... 
FitzHugh–Nagumo model | Amplitude–frequency curves | Primary resonance | Van der Pol oscillator | Fractional-order derivatives | FitzHugh-Nagumo model | 2 KINDS | PATTERNS | Amplitude-frequency curves | MECHANICS | ELECTROENCEPHALOGRAM | DUFFING OSCILLATOR | IMPULSES | MATHIEU EQUATION | ROSE NEURAL-NETWORKS | THEORETICAL-MODELS
Journal Article
Communications in Contemporary Mathematics, ISSN 0219-1997, 02/2018, Volume 20, Issue 1, p. 1750022
We consider a class of Hill equations where the periodic coefficient is the squared solution of some Duffing equation plus a constant... 
Duffing equation | Hill equation | nonlinear beam equation | stability | MATHEMATICS | MATHEMATICS, APPLIED | STABILITY REGIONS | Mathematics - Classical Analysis and ODEs
Journal Article
Results in physics, ISSN 2211-3797, 03/2020, Volume 16, p. 102816
•Perturbed Shrödinger equation with Kerr law nonlinearity and Kundu-Mukherjee-Naskar equation are considered... 
Kundu-Mukherjee-Naskar equation | Cubic Duffing equation | New extended algebraic method | Shrödinger’s equation
Journal Article
Positivity, ISSN 1385-1292, 9/2019, Volume 23, Issue 4, pp. 779 - 787
... Liénard equation with a indefinite singularity $$\begin{aligned} x''+f(x)x'+\frac{b(t)}{x}=p(t), \end{aligned}$$ x ′ ′ + f ( x ) x ′ + b ( t ) x = p ( t ) , where $$b... 
Positive periodic solution | 34B16 | Operator Theory | 34C25 | Fourier Analysis | Potential Theory | Calculus of Variations and Optimal Control; Optimization | Mathematics | Indefinite singularity | Econometrics | Liénard equation | MATHEMATICS | SUBHARMONIC SOLUTIONS | MULTIPLICITY | Lienard equation | DIFFERENTIAL-EQUATIONS | DUFFING EQUATION | Computer science | Information science
Journal Article
Optical and Quantum Electronics, ISSN 0306-8919, 3/2018, Volume 50, Issue 3, pp. 1 - 13
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 2011, Volume 62, Issue 10, pp. 3894 - 3901
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 05/2019, Volume 266, Issue 11, pp. 6924 - 6962
This work discusses the boundedness of solutions for impulsive Duffing equation with time-dependent polynomial potentials... 
Quasi-periodic solution | Impulsive Duffing equation | Moser's twist theorem | Lagrange stability | MATHEMATICS
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 01/2015, Volume 251, pp. 669 - 674
We study the periodic solutions of the following kind of non-autonomous Duffing differential equation y¨+ay-εy3=εh(t,y,ẏ), with a>0,ε... 
Duffing differential equation | Periodic solution | Averaging theory | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | STABILITY | BOUNDARY-VALUE-PROBLEMS | Mathematical models | Duffing equation | Computation | Mathematical analysis
Journal Article
Indian Journal of Physics, ISSN 0973-1458, 2/2014, Volume 88, Issue 2, pp. 177 - 184
Journal Article
Optical and Quantum Electronics, ISSN 0306-8919, 10/2017, Volume 49, Issue 10, pp. 1 - 11
Journal Article
International Journal of Bifurcation and Chaos, ISSN 0218-1274, 01/2013, Volume 23, Issue 1, pp. 1350014 - 1350015
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 12/2012, Volume 25, Issue 12, pp. 2349 - 2353
In this paper, we derive a class of analytical solution of the damped Helmholtz–Duffing oscillator that is based on a recently developed exact solution for the... 
Damped Helmholtz–Duffing oscillator | Mixed-parity nonlinear oscillator | Asymmetric behavior | Quadratic nonlinearities | Damped Helmholtz-Duffing oscillator | MATHEMATICS, APPLIED | INTEGRABILITY | OSCILLATOR | Mathematical analysis | Oscillators | Exact solutions
Journal Article
Applied Mathematical Modelling, ISSN 0307-904X, 08/2015, Volume 39, Issue 16, pp. 4607 - 4616
Exact analytical solutions for a family of autonomous ordinary differential equations arising in connection with many important applied problems such as a... 
Jacobian elliptic functions | Nonlinear Schrödinger equation | Exact analytical non-singular solutions | Duffing oscillatory equation | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | Nonlinear Schrodinger equation
Journal Article
Meccanica, ISSN 0025-6455, 7/2015, Volume 50, Issue 7, pp. 1841 - 1853
.... The mechanical response in deterministic situation is described by the Duffing equation, whose numerical solution is obtained with the Runge–Kutta... 
Microsystems | Symbolic computing | Nonlinear vibration | Civil Engineering | Stochastic perturbation technique | Mechanics | Automotive Engineering | MEMS | Microresonators | Mechanical Engineering | Duffing equation | Physics | MECHANICS | SYSTEMS | Algebra | Vibration | Algorithms | College teachers
Journal Article