We analyze a Rayleigh type of oscillator, called the Alpazur oscillator, whose bias circuits are switched periodically. We first present a general computational method for finding a bifurcation point for a nonlinear dynamical system with interrupted characteristics. If this system has a chaotic attractor, we also try to stabilize a target unstable periodic orbit embedded in the attractor. We then apply this general methodology to the Alpazur oscillator and show both numerical and experimental results.

19.1 Introduction

In this chapter, we consider a nonlinear dynamical system with interrupted characteristics that exhibits chaos as shown in Fig. 19.1, where the dynamics of the system are abruptly changed when the trajectory reaches ? _i( i = 0,1,2 , m ? 1). In electric circuits, these systems are easily realized by switching elements, e.g., relays, comparators, diodes, and so on. One feature in this study is that bifurcation phenomena and chaos control are discussed in the nonlinear interrupted electric circuits.

Figure 19.1: Example of the dynamical behavior of the trajectory of a nonlinear dynamical system containing a state-dependent switch.

Over the past years, a great deal of studies have been devoted to piecewise linear systems. Periodically interrupted electric circuit ^[1], Chua's...