# Tagged Questions

In dynamical systems, the motion of a particle in some geometric space, governed by some time dependent rules, is studied. The process can be discrete (where the particle jumps from point to point) or continuous (where the particle follows a trajectory). Dynamical systems is used in mathematical ...

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### Polar coordinates for vector field to find sticking flow

I am currently working on an impacting system which is basically just a spring damper and a circular enclosure. Because of the rotational symmetry of the problem I need the vector field in polar ...
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### What is this bifurcation of a fixed point of a two-dimensional diffeomorphism with two parameters?

Suppose I have a diffeomorphism of a plane, $$\bar{x} = F(x,s,t)$$ where $x \in \mathbb{R}^{2}$ and $s \in [a,b] \subset \mathbb{R}$ and $t \in I_{2} \subset{ \mathbb{R}}$ are parameters. Suppose ...
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### What does 'dissipative PDE' means?

Can you give me an idea what is meant with dissipative partial differential equations? I am no phycist (and do not know the difference between initial energy to final energy), but wikipedia told me ...
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### How to pass from an ODEs system to reactions?

I have the following system: $$\frac{dx}{dt}=a_1+\frac{b_1x^n}{K_1^n+x^n}-gxy-d_1x,$$ $$\frac{dy}{dt}=a_2+\frac{b_2x^m}{K_2^m+x^m}-d_2y,$$ where $a_1,a_2,b_1,b_2,K_1,K_2,g,d_1,d_2,n,m$ are real ...
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### time-$t$ flow map of vector field

I met the following expression in some article "... where $\Phi_t$ is the time-1 flow map of the Hamiltonian vector field produced by the Hamiltonian function $H$ = ..." I haven't met any explicit ...
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### Computational Methods for Determining Stability

For a nonlinear system $\dot{x} =f(x,\alpha)$ where $\alpha$ is a parameter, with fixed points $x^*$ such that $f(x^*,\alpha) = 0$, what methods are there for computationally determining the stability ...
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### Analysing the modes of a signal with Laplace transform

If I have a linear dynamical system (assume continuous time for the time being) I can create the transfer function, let's say: $$\frac{1}{(s+a_1)(s+a_2)}$$ and the pole-zero map (this one is for e.g. ...
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### Clarification on asymptotically stability of dynamical systems

I'm wondering if someone can provide a clarification between 2 seemingly opposing definitions from reputable sources on dynamical systems! My Russian textbook, "Dynamical Systems I: Ordinary ...
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### An integral involving a dirac

Let $x(t)$ a process with a differentiable trajectory. How do you understand $\int_0^t |\dot{x}(s)| \delta_{x(s) = 0} d s$?
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### Why is cos and sin used in plotting this phase portrait

I'm plotting the phase portrait of the following system of ODE: $\frac{dx}{dt} = x + 3 y$ $\frac{dy}{dt} = -5 x + 2 y$ The code I have in matlab: ...
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### Finding explicit solution to 2D system of ODE's

In my studies of dynamics, I came across this ODE system given by: $\dot{x} = -A \frac{\pi}{k}\cos{(\pi y)}\sin{(kx)}$ $\dot{y} = A\sin{(\pi y)}\cos{(kx)}$ where A and k are two non ...