QUALITATIVE-ANALYSIS OF THE DYNAMICS OF THE TIME-DELAYED CHUAS CIRCUIT

Several variants of the Chua's circuit have been recently proposed in order to enlarge the class of nonlinear phenomena that can be generate d by relatively simple circuits, In particular, Sharkovsky et al. prop osed the so called time-delayed Chua's circuit (TDCC), where the origi nal lumped LC resonator is substituted by an ideal transmission line, thereby generating an infinite dimensional system, The TDCC has been s tudied in details in the absence of the capacitor C. the only lumped d ynamic element left in the circuit, This paper studies the effects of the presence of C on the dynamics of the circuit. After recasting the circuit equations in a suitable normalized form, their characteristic equation is theoretically investigated and the regions in the paramete r space where all the eigenvalues have negative real part are exactly evaluated along with all the possible qualitative eigenvalue distribut ions, This analysis allows for a qualitative description of the TDCC d ynamics in presence of the capacitor C. In particular, it is shown tha t, for particular sets of circuit parameters, an even small value of C . e.g., a parasitic element, may completely change the behavior of TDC C and that, on the other hand, any TDCC, exhibiting the period-adding phenomenon for C = 0. still continues to present this phenomenon even if a small capacitor C is added to the circuit.