Duffing equation - Wikipedia
The Duffing equation (or Duffing oscillator), named after Georg Duffing (1861–1944), is a non-linear second-order differential equation used to model certain damped and driven oscillators.
Duffing oscillator - Scholarpedia
2011年10月21日 · Duffing oscillator is an example of a periodically forced oscillator with a nonlinear elasticity, written as \[\tag{1} \ddot x + \delta \dot x + \beta x + \alpha x^3 = \gamma \cos \omega t \ ,\] where the damping constant obeys \(\delta\geq 0\ ,\) and it is also known as a simple model which yields chaos, as well as van der Pol oscillator .
The case with k1<0 and k2>0 is called “Duffing’s two-well oscillator” and models a ball rolling along a trough having two dips with a hump in between. All of these cases can exhibit chaos with the right parameter values. For example: Simulink model and phase plot shown below.
MATHEMATICA tutorial, Part 2.3: Duffing oscillator - Brown …
5 天之前 · In this section, we analyze differential equation modeling Duffing oscillator, named after Georg Duffing (1861--1944). It provides an example of a periodically forced oscillator with a nonlinear elasticity. The Duffing equation is an example of a dynamical system that exhibits chaotic behavior.
Here we consider an intermediate situation where the dynamics is described by a single ordinary differential equation, called the Duffing equation. In order to get chaos in such a simple system, we will need to add both a driving force and friction. First of all though we just consider the basic equation without these extra features.
The Duffing Oscillator - SpringerLink
The Duffing oscillator is one of the prototype systems of nonlinear dynamics. It first became popular for studying anharmonic oscillations and, later, chaotic nonlinear dynamics in the wake of early studies by the engineer Georg Duffing [1].
Georg Duffing’s Equation | Galileo Unbound
2019年3月20日 · Although Duffing had spent considerable attention in his book to the quadratic term for an asymmetric oscillator, the term “Duffing Equation” now refers to the stiffening and softening problem rather than to the asymmetric problem.
The Duffing Oscillator Equation and Its Applications in Physics
2021年11月30日 · In this paper, we solve the Duffing equation for given initial conditions. We introduce the concept of the discriminant for the Duffing equation and we solve it in three cases depending on sign of the discriminant. We also show the …
The Dulling oscillator is one of the prototype systems of nonlinear dynamics. It first became popular for studying anharmonic oscillations and, later, chaotic nonlinear dynamics in the wake of early studies by the engineer Georg Dulling
A 40-year journey towards understanding the Duffing oscillator
2023年5月30日 · The Duffing oscillator, named after the German engineer Georg Duffing, is a simple but prototypical model system in nonlinear physics.
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