# Questions tagged [basins-of-attraction]

The basin of attraction of a given attractor is the set of initial conditions leading to convergence to that attractor.

37 questions
Filter by
Sorted by
Tagged with
34 views

### Fokker-Planck: uniqueness and attractiveness of stationary distribution (gradient systems)

consider the Langevin equation ($N$-dimensional) with nonlinear drift term but expressible as a gradient of a function $U(\vec{x})$. Namely, consider the stochastic process described by the set of ...
52 views

### Plotting the bifurcation diagram for Ikeda map

I'm trying to plot the bifurcation diagram for Ikeda map. I wrote a code in Python to get the points of this diagram, but it seems that for $u > 1$ the points diverge and my code doesn't work ...
57 views

### the relation between chaos and fractal basin

Does fractal boundary of basin of attraction has something to do with chaos? I think fractal boundary must lead to chaos, and how about the other way round?
• 417
39 views

### Does dynamical system has volume preserving property in basin of attraction?

I have a question on the basin of attraction: Does the dynamic flow on every bounded region inside of a basin of attraction has volume preserving property?
• 417
40 views

• 1
1 vote
32 views

### Can I say a manifold is partitioned by the basin of attractions?

For smooth continuous dynamical system, $$\dot{x} = f(x),$$ on manifold $\mathcal{M}$, can I say it is partitioned by countably many basins of attraction? Motivation I want to prove something which ...
1 vote
138 views

• 762
1k views

### Basin of attraction of the fixed map $f(x) = x-x^3$

Prove that the interval $(-\sqrt 2 ,\sqrt 2 )$ is the basin of attraction of the fixed point $0$ of the map $f(x)=x-x^3$, for $x \in \mathbb{R}$. How one would prove this? In the examples I've seen ...
6k views

### Newton's method — for which initial guesses does it converge?

We've got a function: $f : \Bbb R \to \Bbb R$ defined by $f(x) = x^3 - 9$. Let $x^*$ be its root, which means $f(x^*) = 0$. We want to find approximation for $x^*$ using a Newton's method. There ...
• 1,507
1k views

### Does every basin of attraction contain a critical point?

Years and years ago, back when I first became interested in fractals [but didn't know much about anything], I vaguely remember coming across an interesting theorem. The gist of it was that "every ...
• 5,597