A computational approach analyzing global dynamics

We describe the lattice structure of attractors in a dynamical system and the lifting of sublattices of
attractors, which are computationally less accessible, to lattices of forward invariant sets and attracting
neighborhoods, which are computationally accessible. We also show how the use of these algebraic
structures of lattices to help us to capture the information about underlying dynamical system in a more
elegant way and with lesser computational cost. For example, they can be used to develop a much
efficient algorithm to compute a global lyapunov function
that describes the overall gradient dynamics.