# 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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### Is Singularity corresponds to null space and are forces causing singularity are some transformation matrix?

Some random thoughts: (Disclaimer: i am a complete noob in physics). I was studying linear transformations from linear algebra and just got this thought that there might be some set of transformation ...
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### How are the Bloch equations non-linear?

This question is similar to the following, but I have expanded the question moderately: Nonlinearities arising from linear equations The Bloch equations are described by the following vector equation (...
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I'm having trouble solving the following problem. I've designed a control system for a quadcopter, my design is built upon a nonlinear model in the affine form: $$\dot{x}=f(x)+g(x)u$$ The system ...
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### Solution to non-linear differential equation, non-linear oscillator

Is there any way to find an analytical solution to this equation? $$m \ddot{x}(t) = B_0 \left( \frac{1}{x(t)^4} - \frac{1}{(L-x(t))^4} \right)$$ this is supposed to describe a magnetic oscillator ...
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### Phase space portrait for dynamical system with Bifurcations

I have this dynamical system $$x'=y, y'=-x^3-y+mx$$ and I want to draw the phace space diagram for $m=-1/8, m=1/4,$ the bifurcation points. 1st of all I cant find what kind of bifruction I have( I go ...
1 vote
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### Four-wave mixing and modulation transfer spectroscopy: why do sidebands appear on the probe?

I'm trying to understand modulation transfer spectroscopy in simple terms. For those unfamiliar with it, this article gives a very good summary. To sum it up, two counterpropagating beams, a pump and ...
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### Why must operators in QM be linear?

Why must all operators in QM be linear (and therefore able to be represented by matrices). What is the physical reasoning behind this? Is it be possible that the non-unitary nature of quantum collapse ...
1 vote
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### Why is synchronisation only possible for self-sustaining oscillators

A self sustained oscillator is any oscillator which obeys the following 3 key properties (Balanov 2009): They do not damp They are capable of oscillating without being driven by an external force. ...
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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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### 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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1 vote
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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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### Particle and metric redefine in action corresponding and beyond conformal transformation

let us beginning form action with system of gravity and scalar field. $$S=\int d^d x \sqrt{g}(R-g^{ab}\partial_a \phi \partial_b \phi-V {(\phi)} )$$ and redefine metric  \tilde{g_{ab}} = f(g_{ab},\...