[SciPy-user] Eigenvalues of the Floquet matrix

Nils Wagner nwagner@iam.uni-stuttgart...
Sat Mar 14 15:21:46 CDT 2009

Hi all,

I am interested in the stability of time periodic ODE's of
the form

\dot{y} = A(t) y,  A(t)=A(t+T)          (1)

I have used scipy.integrate.ode to compute the eigenvalues
of the Floquet matrix. See attachment for details.

The eigenvalues \lambda of the Floquet matrix are called 
Multipliers of system (1) possess symmetry: If \lambda is 
multiplier, then 1/\lambda is also a multiplier.

The system is stable iff all eigenvalues are inside
the unit circle.

However, I cannot reproduce the symmetry of the
numerical multipliers computed by scipy, e.g.

>>> evals
array([ -2.55239771e-02+0.j        , 
         -2.39509330e-02-0.99921743j,  -3.85602951e+01+0.j 
>>> 1./evals
array([ -3.91788472e+01-0.j        , 
         -2.39746890e-02+1.00020852j,  -2.59334115e-02-0.j 

How can I improve the numerical results concerning the
symmetry ?

The computation of a stability chart is a time-consuming
task even for low dimensional systems.

How can one accelerate the process ?

Is it possible to parallelize the integration, I mean
each processor could solve (1) for a new set of
initial conditions ?

Any pointer would be appreciated.

BTW, the example is taken from a recent paper by 

Thanks in advance.



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