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Results tagged with eigenvalues
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user 6358
Questions on symbolically or numerically determining the eigenvalues of matrices (Eigenvalues, Eigensystem) or differential equations (DEigenvalues, DEigensystem, NDEigenvalues, NDEigensystem) in Mathematica. Also includes determining the eigenvalues of differential equations with DSolve or NDSolve.
0
votes
Accepted
How to find periodic steady state of symbolic matrix in Mathematica?
See e.g. section 4.4 of these notes.
a := {
{-1, 1, 0, 0, 0, 0},
{1, -2, 1, 0, 0, 0},
{0, 1, -2 + e, 1 + e, 0, 0},
{0, 0, 1 - e, -2 - e, 1, 0},
{0, 0, 0, 1, -2, 1},
{0, 0, 0, 0, 1, -1}
}
N[Eigenvalues …
- 20.4k
10
votes
Tracking Eigenvalues Through a Crossing
Also note that this gives a single eigenvector in the case of repeated eigenvalues. Surprisingly this doesn't cause any problems at the crossings. … B0 = 0.1; (* initial parameter value *)
λ0s = Eigenvalues[H /. …
- 20.4k
5
votes
Accepted
"Arnoldi" method for Eigenvalues inside FindRoot
NumericQ] :=
Eigenvalues[mat[x], -1,
Method -> {"Arnoldi", "Criteria" -> "RealPart",
"Shift" -> -1000}];
Print[Plot[{fu[x], lowest}, {x, -100, 100}, PlotRange -> All]];
Return[ …
- 20.4k
8
votes
Tracking Eigenvalues Through a Crossing
NumericQ] := Check[
Eigenvalues[mat, 1, Method -> {"Arnoldi", Shift -> ic}][[1]],
ic, Eigenvalues::ssing];
Next, generate a list of initial solutions at a nice parameter value.
λ0s = Eigenvalues[ … One note (not relevant to this problem): this fails if the eigenvalues are complex. …
- 20.4k
1
vote
Accepted
Find the parameter values for my matrix for it to have imaginary eigenvalues
NumericQ] := Max[Re[Eigenvalues[a /. u -> v]]]
Plot[maxev[u], {u, -10, 10}, PlotRange -> {0, 10}]
Your 3x3 example matrix doesn't seem to have any points with Re[eigenvalue]=0, so let me modify it: … [a /. bif1]]
Chop[Eigenvalues[a /. bif2]]
(* {-3., 0. + 0.643852 I, 0. - 0.643852 I} *)
(* {-1.5 + 0.479364 I, -1.5 - 0.479364 I, 0} *)
Thus, in this example, bif1={u -> -0.621916} seems to be what …
- 20.4k
9
votes
Sensitivity analysis of parameter on eigenvalues of predator-prey model
Here's a solution using my EcoEvo package, which is designed for just this kind of problem. First, install the package (only need to do this once):
PacletInstall["EcoEvo", "Site" -> "http://raw.githu …
- 20.4k
12
votes
Routh-Hurwitz criterion not giving correct answer when done manually?
I can't say why your approach didn't work, but my RouthHurwitzCriteria function uses a simplified test for 3x3 matrices due to Fuller (1968), which I first learned about from Gandolfo (1997):
There a …
- 20.4k