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duffing

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duffing
duffing, ppl. a. slang. (ˈdʌfɪŋ) [f. duff v.1] 1. That passes off a worthless article as valuable.1862 Lond. Herald 27 Dec. (Farmer) Houses..run up by the ‘duffing’ builder, merely for sale. 2. Counterfeit, rubbishy and offered as valuable.1851 Mayhew Lond. Labour (1861) II. 19 Dealers in ‘duffing f... Oxford English Dictionary
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Georg Duffing
Family and career Georg Duffing was born in 1861 in the Baden town of Waldshut as the eldest son of merchant Christian Duffing and his wife Julie Spies Georg Duffing was buried in Berlin at the Friedhöfe vor dem Halleschen Tor. Duffing held various technical patents in Germany and the USA. wikipedia.org
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Duffing map
The Duffing map (also called as 'Holmes map') is a discrete-time dynamical system. It is a discrete version of the Duffing equation. References External links Duffing oscillator on Scholarpedia Chaotic maps wikipedia.org
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Duffing equation transformation $(t,x) \rightarrow (-t,-x)$ We have the Duffing equation, $\ddot{x}+ λ\dot{x}=x-x^3$, which can also be written as $\dot{x}=y$ $\dot{y}=-U'(x)- λ y=x-x^3-\lambda y $ Show that the tr...
These things can be confusing, but this specific case is quite simple. We impose the substitutions $$ x=-X, \qquad t=-s, $$ which imply $$ \frac{d}{dt}=-\frac{d}{ds},\qquad \frac{d^2}{dt^2}=\frac{d^2}{ds^2}, $$ so that $$ \frac{d^2x}{dt^2}+\lambda \frac{dx}{dt}=-\frac{d^2X}{ds^2}+\lambda\frac{dX}{ds...
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Duffing equation
The Duffing equation (or Duffing oscillator), named after Georg Duffing (1861–1944), is a non-linear second-order differential equation used to model certain The Duffing equation is an example of a dynamical system that exhibits chaotic behavior. wikipedia.org
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duff
▪ I. duff, n.1 (dʌf) [orig. a northern pronunc. of dough: cf. enough.] a. Dough, paste. (dial.) b. A flour pudding boiled in a bag.; a dumpling.1840 R. H. Dana Bef. Mast iv. 7 To enhance the value of the Sabbath to the crew, they are allowed on that day a pudding, or, as it is called, a ‘duff’. 1847... Oxford English Dictionary
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Scribing (cartography)
Corrections can be made by "duffing" (re-coating) the scribe sheet with special duffing liquid. The detail can then be re-scribed. wikipedia.org
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About Duffing equation Is there a relation between Duffing equation and Van der Pol equation? My second question is what is the application(s) of stochastic Duffing equn. in practice ?
Van der Pol is smooth continuous but Duffing has sudden "snap-through" bi-stable behavior like the Belleville spring in the negative stiffness region.
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Stability Systems - Duffing oscillator In the case a=1,b=-1 this is the system: $$ dx=y $$ $$ dy=-x + x^3$$ I have to draw the phase space with the trajectories of the orbits. And I don´t know who to demonstrate the d...
For the critical point at $(0, 0)$ just evaluate the dynamical system close to the origin. For example, take $x = 0.1$, and $y = 0$, you see that at that location ${\rm d y}/{\rm d}t < 0$, that means that a that location $y$ will be decreasing. In other words, the orbit going through $(0.1, 0)$ will...
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Texas's 35th House of Representatives district
It also includes the cities and Census-designated places of La Feria, San Benito, Duffing, La Homa, La Joya, Penitas, and a small percentage of Brownsville wikipedia.org
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Existence of global attractor in duffing equation How to prove the existence and identify global attractor in Duffing equation $$\ddot{x}+\epsilon \dot{x}+x^3-ax=0$$ where $\epsilon >0$ and $a>0$? I found a definitio...
The equation describes a mechanical system with friction/energy dissipation. Or in formulas $$ \frac{d}{dt}\left[\frac12\dot x^2+\frac14(x^2-a)^2\right]=-ϵ\dot x^2. $$ So as long as the particle the system describes is in motion, it will lose energy and move down to one of the minima $x=\pm\sqrt{a}$...
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Multiscroll attractor
-0.6 Other attractors Multiscroll attractors also called n-scroll attractor include the Lu Chen attractor, the modified Chen chaotic attractor, PWL Duffing chaotic attractor Aziz Alaoui investigated PWL Duffing equation in 2000: PWL Duffing system: params := e = .25, gamma = .14+(1/20)i, m0 = -0.845e-1 wikipedia.org
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Hamiltonfunction under a Duffing Oscillator Given is the following oscillator $$\ddot{x} + \lambda\dot{x}=x-x^3$$ I've already rewritten this as a system of first order equations $$\begin{cases} \dot{x} = y \\\ \dot{y...
Instead of the Hamiltonian, I can give you the Lagrangian. In the existence of friction, it is well known to physicists that the following Lagrangian gives the correct equation of motion. $$L[x,\dot{x},t] = e^{\lambda t/m} \bigg(\frac{1}{2}m\dot{x}^2 - U(x)\bigg)$$ $$\Rightarrow m\ddot{x} +\lambda \...
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Multiple-scale analysis
undamped and unforced Duffing equation: which is a second-order ordinary differential equation describing a nonlinear oscillator. The undamped Duffing equation is known to be a Hamiltonian system: with q = y(t) and p = dy/dt. wikipedia.org
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When can a non-autonomous system NOT be re-written as an autonomous system? Consider Duffing's equation $\ddot x + \delta \dot x + \alpha x + \beta x^3 = \gamma \cos{\omega t},$ where $\delta, \alpha, \beta, \gamma$...
Given a non-autonomous system $x'=f(x,t)$, you can introduce new vector function $u(t)=(x(t),t)$ which satisfies the autonomous system $u'=g(u)$ with $g(u)=(f(u),1)$. So the answer is yes, you can always turn a system into autonomous. The implication is that the dimension of the system goes up. And ...
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