# 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.

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### In nonlinear systems with at least 1 asymptotically stable point is it true that every point on the phase plane is in a basin of attraction/separatrix

In differential equations, for a system of autonomous nonlinear differential equations, is it true that if there exists at least one asymptotically stable point, then EVERY point in the phase plane ...
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### Can a function be converted into a Voronoi diagram of its local extremum points and basins of convergence?

Let's say I know the position $e \in \mathbb{R}^N$ of a local extremum point of a non-convex function $f: \mathbb{R}^N \mapsto \mathbb{R}$. Is there an efficient method for finding $K$ closest "...
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### What if the level set of Lyapunov function is disconnected? - when estimating region of attration

Consider $\frac{dx}{dt}=f(x)$, where $x\in\mathbb{R}^n$. Suppose $x=0$ is a stable equilibrium. It is classical way to estimate region of attraction of $0$ by finding a $C^1$ function $V(x)$ such that ...
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### 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 ...
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