The Butterfly Effect is well-known as the sensitivity to initial conditions displayed by some dynamical systems, meaning that a small perturbation to initial conditions can result in a large change to the state of the system after some length of time (dynamical instability).
The Hawkmoth Effect, by analogy, is the sensitivity to structural model formulation, meaning that a small perturbation to the system itself can result in a large change to the state of the system after some length of time (structural instability).
View a picture of a magnificent Poplar Hawkmoth. They also have impressive caterpillars.