  We develop a framework for understanding the difference between strong and
fragile behavior in the dynamics of glass-forming liquids from the properties
of the potential energy landscape. Our approach is based on a master equation
description of the activated jump dynamics among the local minima of the
potential energy (the so-called inherent structures) that characterize the
potential energy landscape of the system. We study the dynamics of a small
atomic cluster using this description as well as molecular dynamics simulations
and demonstrate the usefulness of our approach for this system. Many of the
remarkable features of the complex dynamics of glassy systems emerge from the
activated dynamics in the potential energy landscape of the atomic cluster. The
dynamics of the system exhibits typical characteristics of a strong supercooled
liquid when the system is allowed to explore the full configuration space. This
behavior arises because the dynamics is dominated by a few lowest-lying minima
of the potential energy and the potential energy barriers between these minima.
When the system is constrained to explore only a limited region of the
potential energy landscape that excludes the basins of attraction of a few
lowest-lying minima, the dynamics is found to exhibit the characteristics of a
fragile liquid.
