# A Few Examples of Pictures (Using MATLAB or c++):

Fig.1.116 Van der Pol oscillator for μ=0.2 and μ=1.

Fig.1.117 Van der Pol oscillator for μ=1 and μ=10.

Fig.1.118 Van der Pol oscillator for μ=2.5, [t,y_{1},y_{2}].

Fig.4 Power Spectrum of the variables y_{1} and y_{2} for the van der Pol oscillator for μ=2.5.

Fig.209 Power Spectrum (and lobes) of the logistic attractor for alpha=3.494.

Fig.1.33 Chua autonomous circuit (Chua attractor).

Fig.1.35 Colpitts oscillator (simple chaotic generator).

Fig.1.117d Van der Pol oscillator for μ=0.275, [t,y_{1},y_{2}].

Fig.1.103. 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

With β=10, μ=0.456, η=0.0357

A bleu sky orbit underlying catastrophe, i.e. blue sky bifurcation. For [x,y,z]. (Azimut=0°, Elevation=0°).

Fig.1.103. Blue sky orbit (N. Gavrilov and A. Shilnikov).