# Tag Info

9

I just wanted to a bit more context here, and it is too long for a comment. First, there have always been platform differences in the available features, going back to V1. These were mostly on the FE side, but it's certainly not unprecedented on the language side. For example, CurrentImage was available on Mac and Windows well before it was on Linux. Had ...

1

Conditions 1 and 2 are trivially satisfied. Now we deal with the 3rd condition. We simplify here by multiplication of both sides with denominator and take the RHS to the LHS yielding: B C^3 D^3 + 3 B C^2 D^3 \[Xi] + B C D^4 \[Xi] + B^2 D^3 \[Xi]^2 + 2 B C D^3 \[Xi]^2 + B D^4 \[Xi]^2 + B C^3 D \[Beta] \[Sigma] + B C^2 D^2 \[Beta] \[Sigma] + B C D^3 \[Beta]...

10

I contacted the customer support and got the following reply: "The 'FEAST' method for functions like Eigensystem is part of the Intel MKL library, and as such will not be available to non-Intel CPUs. I have filed an internal suggestion report on this topic, so that methods for including this method on ARM systems can be considered for inclusion in ...

1

We can apply Rouché's theorem. This theorem states for for any two polynomials $f(z)$ and $g(z)$ and any region in the complex plane $K$, if $|f(z) - g(z)| < |g(z)|$ at every point on the boundary of $K$, then $f(z)$ and $g(z)$ have the same number of roots (counting multiplicities) in the interior of $K$. In particular, let's take $K$ to be the unit ...

2

To make the job easier, we shift the eigenvalues by -1. Then the condition reads: 2 eigenvalues <0 and 1 eigenvalue >0. Shifting the eigenvalues can be achieved by subtracting the Identity matrix: m = {{14.6235 (0.0925809 + 0.0378381 (0.0696333 a + 0.256263 b)), -14.6235 (0.0240451 + 0.0378381 (0.0696333 a + 0.264 b)), 0.435909}, {1, ...

7

Your approach didn't work because the last condition cannot be solved easily, that is, you need at least one parameter of degree one to solve without complexity. Then, Chris's routine does work perfectly. However, it is possible to analyze stability if we think about the Hopf bifurcation, and we solve the following equation \label{1} \left| \begin{array}{...

12

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 are extensions to higher-order systems in Murata (1977) that I thought about implementing, but never had the time. Any matrix lovers out there want to help? ...

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