Dynamics of the forced negative conductance series LCR circuit

摘要

In this paper, we make a revisit of a simple LCR circuit introduced earlier in 2005 by Thamilmaran et. al., and present the circuit simulation studies of its dynamics using the PSpice circuit simulator package. This is a simple sinusoidally forced series LCR circuit, employing an ordinary single PN junction diode in conjunction with a negative conductance as its nonlinearity. In circuit theoretic terms, this circuit is a modified form of the forced van der Pol type oscillator and is interesting because it exhibits a dual nature, namely, a forced van der Pol type circuit behaviour and an MLC circuit type behaviour for different parametric ranges. In addition, statistical studies have shown the circuit to possess strong chaoticity. Subsequent works on this circuit have shown the birth of strange nonchaos through four different routes, namely, the Heagy-Hammel route, gradual fractalization route, intermittency route, and Bubbling route. In lieu of these, we look at the circuit afresh and study its dynamics in an exhaustive manner. These studies reveal many new bifurcations and routes to chaos. These results have been verified using hardware experiments in addition to numerical computations.