  Out-of-time-ordered correlators (OTOC) have been extensively used as a major
tool for exploring quantum chaos and also recently, there has been a classical
analogue. Studies have been limited to closed systems. In this work, we probe
an open classical many-body system, more specifically, a spatially extended
driven dissipative chain of coupled Duffing oscillators using the classical
OTOC to investigate the spread and growth (decay) of an initially localized
perturbation in the chain. Correspondingly, we find three distinct types of
dynamical behavior, namely the sustained chaos, transient chaos and non-chaotic
region, as clearly exhibited by different geometrical shapes in the heat map of
OTOC. To quantify such differences, we look at instantaneous speed (IS), finite
time Lyapunov exponents (FTLE) and velocity dependent Lyapunov exponents (VDLE)
extracted from OTOC. Introduction of these quantities turn out to be
instrumental in diagnosing and demarcating different regimes of dynamical
behavior. To gain control over open nonlinear systems, it is important to look
at the variation of these quantities with respect to parameters. As we tune
drive, dissipation and coupling, FTLE and IS exhibit transition between
sustained chaos and non-chaotic regimeswith intermediate transient chaos
regimes and highly intermittent sustained chaos points. In the limit of zero
nonlinearity, we present exact analytical results for the driven dissipative
harmonic system and we find that our analytical results can very well describe
the non-chaotic regime as well as the late time behavior in the transient
regime of the Duffing chain. We believe, this analysis is an important step
forward towards understanding nonlinear dynamics, chaos and spatio-temporal
spread of perturbations in many-particle open systems.
