Bifurcation sets in forced rayleigh oscillator containing a diode

Abstract

AbstractThe forced Rayleigh equation is known as the differential equation for which the existence of the aperiodic solution is shown for the first time. From the viewpoint of the history of the research of chaos, it is very important to examine the bifurcvation in this equation. the authors considered the forced Rayleigh oscillator containing a diode. By considering the limit α → ∞ for a parameter α contained in the system, the ideal diode constrained equation is defined. Then, the rigorous analysis of the bifurcation phenomenon is made for the forced Rayleigh oscillator.This paper considers the forced Rayleigh oscillator containinig a large parameter α and shows that the bifurcation concerning the chaos generated in the oscillator can be accounted for by the ideal diode constrained equation by constructing and comparing the detailed bifurcation diagrams for the two systems.