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Plot a phase portrait of two complex ODE

Ser Man
Posted 8 years ago

Hi, I have two ODE's, which list as:

y = x' and y' = -ibx -c

where b and c are exponential constants. How can I generate a phase portrait of this ODE in wolfram alpha?

Thanks!
POSTED BY: Ser Man
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Ser Man
Ser Man
Posted 8 years ago

Dear Michael, thanks for the code. I will try it on Mathematica directly, however I have a final question,

you say a is not there in the ODE, which is true, however, it is in your code:

Subscript[a, b

iand it is further down given along with b and c, which are in the equation, as a defined value (1). Where is a in the system of the ODEs, if it is included here in your code, and if it is not-related to the ODE, what is the a for?

Thanks!

PS: I take I can replace b and c with some different values.

Cheers
POSTED BY: Ser Man
POSTED BY: Michael Rogers
POSTED BY: Michael Rogers
Ser Man
Ser Man
Posted 8 years ago

Thanks Michael. If you set b = c = 1 in:

[ a, ib; 1, 1]

it would give:

[ a, ic; 1, 1]

Did you include a? Can I try this command somehow? I have some experimental values for a and b. a would be 1^-68 and b would be 2^7. So a and b (c) differ so much, that one may wonder if it is plottable at all.

Thanks!
POSTED BY: Ser Man
Ser Man
Ser Man
Posted 8 years ago

Hi Michael, it can be simplified to:

y = x' and y' = -icx

where c is a real number, and i is the imaginary unit. According to the signs of the eigenvalues, and their relationship to the matrix determinant of this system, it should be a source spiral, evolving out from the unstable origin.

The matrix is:

[ a, ib; 1, 1]

where a and b are combined to c in the simplified ODE.

The eigenvalues and eigenvectors suggest thus an outward spiral

Thanks
POSTED BY: Ser Man

Can you give an example of the kind of output you want? Like an image off the internet, or a pic of a hand drawing. It seems to me that the phase space is ${\bf C}^2$, which is 4-dimensional, I don't have a good idea how one would represent such a space graphically.
POSTED BY: Michael Rogers
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