  We study the statistical fluctuations of Lyapunov exponents in the discrete
version of the non-integrable perturbed sine-Gordon equation, the dissipative
ac+dc driven Frenkel-Kontorova model. Our analysis shows that the fluctuations
of the exponent spacings in the strictly overdamped limit, which is nonchaotic,
conforms to the \textit{uncorrelated} Poisson distribution. By studying the
spatiotemporal dynamics we relate the emergence of the Poissonian statistics to
Middleton's no-passing rule. Next, by scanning over the dc driving and particle
mass we identify several parameter regions for which this one-dimensional model
exhibits hyperchaotic behavior. Furthermore, in the hyperchaotic regime where
roughly fifty percent of exponents are positive, the fluctuations exhibit
features of the \textit{correlated} universal statistics of the Gaussian
Orthogonal Ensemble (GOE). Due to the dissipative nature of the dynamics, we
find that the match, between the Lyapunov spectrum statistics and the universal
statistics of GOE, is not complete. Finally, we present evidence supporting the
existence of the Tracy-Widom distribution in the fluctuation statistics of the
largest Lyapunov exponent.
