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

**Convo.swf:** Schematic representation of the convolution of an arbitrary curve (i.e. signal) with a wave function which moves along the signal. Observe how the wave function highlights the variations of the signal. (12').

**HopfBif.swf:** Orbit and Hopf Bifurcation of the Nonlinear Dynamical System: dz/dt= (μ+iγ)z-z|z|^{2} z=complex: (Hopf), γ=fixed.μ=-0.2,..,2.2 [μ-abscissa, x_{1}, x_{2}].

**BasicHopf.swf:** Hopf bifurcation for the system:

(1). dx_{1}/dt = x_{2} + x_{1} [ μ - x_{1}^{2} - x_{2}^{2} ]

(2). dx_{2}/dt = - x_{1} + x_{2} [ μ - x_{1}^{2} - x_{2}^{2} ]

where μ varies as follows: μ= -1,..,2. (03')

**orbitDyn2.swf:** Orbit and Bifurcations of a Nonlinear Dynamical System according to μ,γ. (γ=-1,...,1, μ=-0.5,..,3). [μ-abscissa, x_{1}, x_{2}]. **ATTENTION** - Consider as an exercise the question: *Is this simulation valid or not?* (cf. corresponding Matlab m-file, "Dynamic2.m") (13'):

**slw.swf:** Reference Solow model while the parameter s varies from 0.1 to 0.152. (08')