Effects of Symmetry-Breaking on the Dynamics of the Shinriki’s Oscillator

Description

Symmetry is an important property found in a large number of nonlinear systems. In this chapter, we investigate the dynamics of the well-known Shinriki’s oscillator both in its symmetric and asymmetric modes of operation. Instead of using the classical approximate cubic model of the Shinriki’s oscillator, we propose a close form model by exploiting the Shockley exponential diode equation. The proposed model takes into account the intrinsic characteristics of semiconductor diodes forming the nonlinear part. We address the realistic issue of symmetry-breaking by considering different numbers of diodes within the two branches of the positive conductance. The dynamics of the system is investigated by exploiting conventional nonlinear analysis tools. In the symmetric mode of operation, the system experiences coexisting attractors, period-doubling route to chaos, and merging crisis. The symmetry breaking analysis yields two asymmetric coexisting bifurcation branches each of which exhibits its own sequence of bifurcations to chaos when monitoring the main control parameter. The theoretical results are validated by carrying out laboratory experimental studies of the physical circuit.