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A Few Animations (Using MATLAB): Shock-Wave Flash (SWF)


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vdp3D1, vdp3D2, vdp3D, vdpPwS.swf: Behavior of the Van der Pol oscillator. The system is written:
             dY/dt = [y2 ; μ(1-y12) y2-y1]
for μ varying from 0 to 2.5.
(1) [t,(y1,y2)], (2) [y1,y2], (3) [t,y1,y2], (4) Spectra.
The last movie above shows the Power Spectrum of the variables: y1 and y2 for the previous van der Pol oscillator where μ varies from 0 to 2.5. (16')


vdp3DL.swf: Behavior of Van der Pol oscillator:
             dY/dt = [y2 ; μ(1-y12) y2-y1]
for μ = -0.8,....,2.4. (22')


BSC1.swf : The first example of the specific equations undergoing the catastrophe was given by N. Gavrilov and A. Shilnikov:
(1). dx/dt = x (2+μ-β(x2+y2))+z2+y2+2y
(2). dy/dt = -z3-(1+y)(z2+y2+2y)-4x+μy
(3). dz/dt = (1+y)z2+x2
where β varies between 0.18 and 10, and μ=0.456, η=0.0357. A bleu sky orbit underlying catastrophe, i.e. blue sky bifurcation. For [z,y,x]. (Az.=0, El.=0). (1'' 05').


CHsignals.swf: Cohen class Time-Frequency Distribution of a signal that consists of (1) two slighly different Gabor atoms whose internal frequencies progressively increase, (2) a Dirac, (3) a sinusoid, (4) a noise that increases at each sequence repetition.(23').


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