In this talk we introduce an algorithmic method for the analysis of the global structure of dynamics in a dynamical system generated by a continuous map in R^n. The recurrent dynamics is captured in a Conley-Morse decomposition, leaving gradient-like dynamics in the remainder of the phase space. With the help of a rectangular grid in R^n, the generator of the dynamical system is represented in terms of a multivalued combinatorial map. The analysis of dynamics is done on a combinatorial level with fast graph algorithms. Automatic homology computation allows one to compute the Conley index which is a topological invariant that allows to reconstruct certain properties of invariant sets found in a combinatorial way. Moreover, if an n-parameter family of dynamical systems is considered, then using outer approximations of dynamics provides an algorithmic method to prove certain continuation results, as well as to detect possible bifurcations. A nonlinear Leslie population model will be used as a sample dynamical system which illustrates the effectiveness of this approach.