All Questions
Tagged with nonlinear-dynamics nonlinear-analysis
44
questions
1
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0
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35
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How to accurately average a function with a nonlinear response?
I am a physics PhD student working in optics and I have a bit of a weird problem that I am trying to sort out and I'm hoping you math folks can help me with.
Without boring you with the experimental ...
0
votes
0
answers
10
views
Example 1.2 Nonlinear Control Khalil
$f( x) =\begin{bmatrix}
x_{2}\\
-sat( x_{1} +x_{2})
\end{bmatrix}$
is not continuously differentiable on $R^2$. Using the fact that the saturdation function sat(.) satisfies $|sat(\eta)-sat{\xi}|$, we ...
- 79
0
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0
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37
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Nonlinear Dynamics and Chaos Strogatz Question 4.4.3
Over dampened Pendulum System:
$$
mL^{2}\ddot{\theta } +b\dot{\theta } +mgL\sin \theta =\Gamma
$$
First order approximation:
$$
b\dot{๐}+mgL\sin{}๐=ฮ
$$
Nondimensionalize, diving through by mgL:
$$
...
- 79
0
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0
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76
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Singularity of a non- linear second order ODE
I have the encountered a singularity in the equation below .
$$
y^{\prime \prime}(x)+\frac{2}{x} y^{\prime}+\left[y-\left(1+\frac{2}{x^2}\right)\right] y(x)=0, \quad 0<x<+\infty,
$$
with ...
0
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0
answers
22
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How to visualize low-dimensional torus in a high-dimensional system?
I have a system of very high-dimensions (1000s of independent variables), but I could show that the dynamics is attracted to a 1D limit cycle or a 2D torus (with commensurate frequencies, so still ...
0
votes
0
answers
94
views
What should I prove to show the states lie within a compact set?
I'm trying to prove the local stability of a nonlinear system and got the following inequality.
$
\|x(t)\|\leq c_1\|x(t_0)\|\exp(-c_2(t-t_0))+c_3\epsilon_m\cdots
$(i)
where $c_1, c_2, c_3$ are ...
- 165
1
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0
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40
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Existence of all stable nonlinear system.
Consider a nonlinear dynamical system that evolves with a continuously differentiable vector field that is there exists a compact set within which the solution trajectories exist and are unique. Is it ...
0
votes
1
answer
93
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Critical points of an autonomous dynamical systems depending on a parameter
Consider the autonomous dynamical system:
$$
\left\{
\begin{array}{l}
\dot{x}=x+y-x^3-\alpha xy^2\\
\dot{y}=y-x-x^2y-y^3
\end{array}
\right.
$$
Prove that $(0,0)$ is the unique critical point if $\...
0
votes
0
answers
26
views
Which methods apply best in the analysis of non-linear phenomena?
I am going to set up my Bachelors project in analysis of non-linear wave phenomena, and I am planning to study plots and graphs of nonlinear spectra.
In this context, I am quite familiar with the ...
- 2,973
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116
views
Can someone help to solve a non-linear ODE using the Runge-Kutta method?
I am doing a literature survey on charged particle dynamics. In a paper the plots between the parameters $(r, \theta, \phi)$ as $r$ vs $\theta$, $\phi$ ($\theta$ vs $\phi$) of the equation :
$$
\frac{...
0
votes
0
answers
35
views
How can I find closed loop dynamics of this system?
There is controller, where $a>0$. Now, if $v>0$, then $u = \ddot\theta(t)$ and if $v<0$, then $-u=\ddot\theta(t)$. However, how can I detect whether $v$ is positive or negative?
1
vote
0
answers
115
views
How Achieve This Specific Non-Linear Mapping
Let's say in a computer program, we have a Slider whereby a user selects a value.
The slider widget itself produces a value, X, from 0.0 to 1.0.
This value then maps to some other range.
Most people ...
user636811
4
votes
1
answer
209
views
2D bifurcation problem
I come across this problem which is about bifurcation. I am trying to take all the cases. I am expecting Hopf bifurcation to occur here but the last case I could not find the fixed point. Could you ...
- 1,575
2
votes
2
answers
93
views
3rd orderCanonical form of nonlinear dynamical system
I am have been solving this problem since a month. I solved a more difficult ones but I do not know why I stuck at this one. There is a clue I can not understand. I solved the first point and stuck ...
- 1,575
0
votes
1
answer
129
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Linearization of system of Nonlinear reaction diffusion equation
I came across many problems in my course and I solved them but the forth one, it seems the hardest for me. I will show the problem I want to solve at first, after that I will show my solution for ...
- 1,575