# Questions tagged [non-linear-systems]

The term non-linear or nonlinear has several definitions but is generally used to describe a system that cannot be approximated by a superposition principle or perturbative approach.

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### Non-linear dynamics

I am confusing between chaotic attractor and strange attractor. I think strange attractor also is related to nonlinear dynamics. Then what is the difference between chaotic attractor and strange ...
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### Questions about Taylor Series Expansion of an Effective Potential [closed]

I was reading a paper and I had a question about it. Here is the relevant part of the paper Here is what I have understood so far: The authors start off with a hamiltonian which describes a particle ...
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### How an applied magnetic field breaks the inversion symmetry in a centrosymmetric system?

I want to understand why magnetic dipole transition breaks the inversion symmetry in a centrosymmetric system and gives rise to second-order nonlinearity.
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### Can this problem be treated in purely mathematical way other than the graphical way? [migrated]

Problem Statement: I attempted all the parts. For part (a), $E_1 = P + R + S$, so $\dot E_1 = \dot P + \dot R + \dot S$. Plugging these values and rearranging the terms would get the desired ...
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### Higher order nonlinear ultrasonic signals

With nonlinear ultrasound, the higher harmonic frequencies are used, for example, to identify defects in materials. Usually the second and third harmonic frequencies are used. If higher orders are ...
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### Born-Infeld equation with a coefficient: which phenomena it describes?

Let us consider the well known Born-Infeld equation $$-{\rm div}\left(\frac{\nabla u}{\sqrt{1-\frac{1}{b^2}|\nabla u|^2}}\right) =g(u).$$ It appears quite naturally in several fields such as ...
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### Is this system linear? [migrated]

$$y(t)=\begin{cases}0 \hspace{4.86cm}x(t)<0\\ x(t)+x(t-2)\hspace{2cm} x(t)\geq0\end{cases}$$ Assuming $C>0$. If $x(t) = C$ is an input, the output will be $2C$, and the output of $-x(t)=-C$ must ...
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### How to generate a PDE from a discrete equation in a rice-pile like model?

I am reading Noise and dynamics of self-organized critical phenomena by Albert Díaz-Guilera Here, on an extension of the rice-pile model by Bak et al demonstrating self-organized criticality. Equation ...
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### Parametric Resonance Analysis using Perturbative approach

I'm reading Parametric Resonance from Landau's Mechanics Text. A similar calculation is done here. Supposing a parametric oscillator given by $$\ddot{x}(t)+\omega_0^2(1+h\cos(\gamma t))x(t)=0$$ It's ...
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### What the response of unstable limit cycles look like?

Stable limit cycles generate oscillations, i was wondering what the unstable limit cycles behaviours look like? From the picture in the left, the system shows a stable limit cycle and it generates ...
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### Chaotic and Ordered Random Boolean Newtorks with a fixed in-degree k and a probability p

I'm working with Random Boolean Networks, I made a python program to show the dynamics of the networks. Before coding the program I study the theory and it says that the in-degree k and the ...
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### Higher order nonlinear stress definition

For the nonlinear case, I often find the following definition for the mechanical stress: $$\sigma=E_2\epsilon+E_3\epsilon^2$$ The parameters $E_2$ and $E_3$ are called "elastic modulus" or &...
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### How chaotic is the double-pendulum if the arms are not perfectly rigid?

The double pendulum is a famous example of a chaotic system. It consists of one pendulum hanging from the end of another pendulum, which in turn hangs from a fixed point. In the traditional version, ...
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### How to perform the multi-scale analysis beyond harmonic oscillations?

I occasionally see this interesting method called multi-scale analysis. From what I understood, it is used to perturbatively solve a perturbed harmonic oscillator, meaning that the equation of motion ...
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### How does the linearity of the Schroedinger equation reflect the interactions?

There is a common lore that linear equations describe non-interacting systems, why non-linearities correspond to non-trivial interactions. My (loose) question is how is that compatible with the ...
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### Uncertainty propagation in dynamical systems

I'm not a physicist, my training is in math and CS. If anything in this question is ill defined or doesn't make sense, say so in the comments and Ill try to fix it. Suppose I have a discrete dynamical ...
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### Electromagnetism, linearity and Feynman diagrams [duplicate]

Currently I am reading Sean Carrol, general relativity. But a thing got me stuck in, I can't understand what he is talking about. We are discussing the introduction to Einstein field equation, so he ...