Chaos Theory for Evolutionary Algorithms Researchers

Abstract

This chapter deals with chaotic systems. Based on the characterization of deterministic chaos, universal features of that kind of behavior are explained. It is shown that despite the deterministic nature of chaos, long term behavior is unpre- dictable. This is called sensitivity to initial conditions. We further give a concept of quantifying chaotic dynamics: the Lyapunov exponent. Moreover, we explain how chaos can originate from order by period doubling, intermittence, chaotic transients and crises. In the second part of the chapter we discuss different examples of sys- tems showing chaos, for instance mechanical, electronic, biological, meteorological, algorithmical and astronomical systems.