  We study the effect of random perturbations in the Human and Nature Dynamics
(HANDY) model. HANDY models the interactions between human population,
depletion, and consumption of natural resources. HANDY explains how endogenous
human--nature interactions could lead to sustainability or collapse in past
societies. We introduce a Gaussian random noise perturbation on the population
change to represent generic external perturbations. The robustness of the
results is investigated with statistical analysis based on probability
distributions of specific events. Our study shows that the results of the
unperturbed HANDY model are robust under small perturbations of $\lesssim$ 10\%
of the Human population. Our results confirm that endogenous dynamics drive the
societal cycles. However, exogenous perturbations, such as floods, droughts,
earthquakes, volcanic eruptions, infectious disease, epidemics, and wars, can
accelerate or delay a collapse cycle.
