Bifurcation Analysis of a Resistor-Double Inductor and Double Diode circuit and a comparison with a Resistor-Inductor-Diode circuit in phase space and parametrical responses

Abstract

Experimental and analytical explorations of an R-2L-2D circuit were carried out. The responses from the ordinary RL-Diode and R-2L-2D circuits were characterized and compared for wide parameter region. As a new circuit, R-2L-2D has an additional inductor and a diode. The circuit had different attractors compared with the ordinary RL-Diode circuit. It was proven that new circuit exhibited wider chaotic regions on the parameter space (i.e. input voltage Vf and frequency f). Both even and odd subharmonic responses were observed following the multiple periodic doublings. The bifurcation analysis revealed to the dominance of feeding frequency by means of the center manifold theory. However periodic and chaotic attractors differed for each circuit, in fact the new circuit generated symmetric trajectories. A detailed investigation proved that the chaotic responses in the proposed circuit could start at the peak-to-peak voltage of Vf= 1.35V at frequency 40 KHz, which was nearly half of the frequency value found for the ordinary circuit. Besides a wide range of chaotic behavior was observed beyond Vf = 0.675 V and f =200 KHz. Chaotic trajectories dominated the dynamics upto f=500 KHz.