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

**vdp3D1, vdp3D2, vdp3D, vdpPwS.swf:** Behavior of the Van der Pol oscillator. The system is written:

dY/dt = [y_{2} ; μ(1-y_{1}^{2}) y_{2}-y_{1}]

for μ varying from 0 to 2.5. **(1)** [t,(y_{1},y_{2})], **(2)** [y_{1},y_{2}], **(3)** [t,y_{1},y_{2}], **(4)** Spectra.

The last movie above shows the Power Spectrum of the variables: y_{1} and y_{2} 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 = [y_{2} ; μ(1-y_{1}^{2}) y_{2}-y_{1}]

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(x^{2}+y^{2}))+z^{2}+y^{2}+2y

(2). dy/dt = -z^{3}-(1+y)(z^{2}+y^{2}+2y)-4x+μy

(3). dz/dt = (1+y)z^{2}+x^{2}+η

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').