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Dec
7
comment Basins of attraction of equilibrium points
As you have shown, the algebraic system $V_x=0,V_y=0$ has four numeric solutions and, if we apply Newton's method to that system, each of those solutions has an interesting basin of attraction. But that is a different question from whether those equilibrium points are attractive under a system of differential equations like $x'=V_x,y'=V_y$.
Dec
7
comment Basins of attraction using Newton's method Part II
I agree with Quantum_Oli - it would be nice to know where this came from. It appears there might be an interesting question here but the image looks like the Julia set of a polynomial - I can't imagine how your non-differentiable function generated it.
Dec
7
comment Basins of attraction of equilibrium points
I'm quite sure that the basins of attraction of Newton's method in two real variables have been well studied; there's an elementary discussion on pages 486-487 of Gil Strang's calculus text. If you're interested in studying the basins of attraction of the smooth dynamical system with a given potential, however, that's quite a different thing. Only one of your equilibrium points is attractive for that system.
Dec
5
comment Basins of attraction using Newton's method
The first thing my answer to that question does is generalize the code to arbitrary functions. I guess that's what @Saurav is referring to.
Dec
3
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Nov
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Nov
13
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Nov
11
comment Can Mathematica Handle Open Intervals? Interval complements?
@alancalvitti True - but, again, I don't think it's hard to roll your own depending on your needs.
Nov
11
comment Can Mathematica Handle Open Intervals? Interval complements?
@alancalvitti There is no such function that I know of, though it should be quite easy to create one using patterns. Something like toInequality[Interval[{a_,b_}], var_] := a<var<b. Then, for example, toInequality[Interval[{1, 2}], x] returns 1<x<2. Of course, you'd still need to decide whether you want open or closed intervals or some combination depending on the situation.
Nov
9
answered Iterating a rational function
Oct
23
comment How to find all graph isomorphisms in FindGraphIsomorphism
Thanks for the info! I've not been using Mathematica of late but, if I find myself needing to study graph theory within Mathematica at some point, I'm sure I'll have a look.
Sep
13
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20
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20
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22
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20
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Jul
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Jul
1
revised Plotting iterated function system images
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