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Chapter 4: Simple Chaotic Models

      https://doi.org/10.1142/9789814719704_0004Cited by:0 (Source: Crossref)
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      Abstract:

      This chapter presents a short study of simple autonomous and non-autonomous systems exhibiting strange chaotic attractors. In particular, the Lorenz and Rössler equations are discussed and the geometrical properties of the chaotic attractors governed by these equations are described. Other examples of autonomous chaotic systems include modified generators with inertial nonlinearity, Chua circuit, systems with quadratic nonlinearities, labyrynth chaos, jerk equations, two-scroll and three-scroll attractors, and Rikitake chaotic attractor.

      Examples of simple non-autonomous systems generating chaos include forced van der Pol equation, Rayleigh equation, Duffing oscillator and single-well oscillator, and externally and parametrically excited oscillators.

      The background given in this chapter is useful while exploring the next chapters since many of the presented and discussed chaotic attractors can also be found in the systems with infinite dimension.