Sensitivity to Initial Conditions of Chaos in Electronics

It has been well known that the sensitivity to the initial conditions can lead to unpredictable trajectory. In this chapter, we discuss the issue on the basis of a Phase Locked Loop circuit with an embedded nonlinear controller. A number of well established techniques for the chaos evaluation have been employed, namely bifurcation, Lyapunov exponent spectrum, fractal basin, etc. The investigations cover not only the basic chaos phenomena, but have also been extended to consider the case of synchronization. As a result, it has been found that this particular controller can broaden the phase lock-in range while its freedom of switching the attractors from chaos to order, or vice versa, can potentially lead to industrial applications.