Many applications involve nonlinear models, but specific parameters are unknown or not directly measurable (this is particularly true for mathematical models in biology). Since the actual dynamics can vary dramatically depending upon the parameters, it is important to be able to identify whether and at what parameter values specific dynamical behavior occurs. Further complicating the issue is that nonlinear systems can both exhibit chaotic dynamics and be structurally unstable for large sets of parameter values. To deal with these issues we are developing techniques to construct databases of the dynamics exhibited by specific multi-parameter systems. The basic idea is to identify and classify crude dynamical structures using graph theoretic and computational topological and algebraic topological techniques that are robust with respect to perturbations induced by numerical and parametrical approximations.