Chapter 3: Introduction to Chaos and Wavelets

This chapter is devoted to definitions of chaos and description of various routes to chaos including the Landau–Hopf scenario, the Ruelle–Takens–Newhouse scenario, the Feigenbaum scenario and the Pomeau–Manneville scenario. The synchronization of chaos is briefly addressed. Quantification of chaotic dynamics via Fourier analysis, Poincaré maps, Lyapunov exponents is described. The Melnikov method to detect strange chaotic attractors is presented. The remaining chapter part is focused on advantages of the wavelet analysis versus the classical Fourier analysis. Properties of different wavelets are illustrated and discussed.