  In this paper we present a generalized analytical solution to the generalized
state equations of coupled second-order non-autonomous circuit systems. The
analytical solutions thus obtained are used to study the synchronization
dynamics of two different types of circuit systems, differing only by their
constituting nonlinear element. The synchronization dynamics of the coupled
systems are studied through two-parameter bifurcation diagrams, phase portraits
and time-series plots obtained from the explicit analytical solutions. The
mechanism of synchronization is realized through the bifurcation of the
eigenvalues as functions of the control parameter in each of the coupled
piecewise linear regions of the drive and response systems. The stability of
the synchronized state for coupled identical chaotic states are studeid through
the {\emph{master stability function}}. Further, {\emph{conditional Lyapunov
exponents}} and {\emph{Kaplan-Yorke dimension}} are obtained to confirm the
synchronized states of both coupled identical and non-identical chaotic states.
The synchronization dynamics of coupled chaotic systems studied through
two-parameter bifurcation diagrams obtained from explicit analytical solutions
is reported in the literature for the first time.
