What does it mean to close a model (dynamic system)?
Some context from a paper by Farmer, Solving and Estimating Indeterminate DSGE Models:
" It is well known that linear rational expectations (LRE) models can have an indeterminate set of equilibria under realistic parameter choices. Lubik and Schorfheide (2003) provided an algorithm that computes the complete set of indeterminate equilibrium, but their approach has not yet been implemented in standard software packages and has not been widely applied in practice. In this paper, we propose an alternative methodology based on the idea that a model with an indeterminate set of equilibria is an incomplete model. We propose to close a model of this kind by treating a subset of the nonfundamental errors as newly defined fundamentals. "
To close the model typically means to add a necessary condition/equation that ensures that there is a solution to the model.
For example consider a simple model of market equilibrium. To compute the equilibrium of a model you would need to know both demand and supply curves. Now, suppose you have rich model of consumers' decision making from which you derive the market demand curve. This is all nice but without supply curve you cannot find the equilibrium price and quantity. So to "close" the model, you have to specify the supply curve.
Going back to your case. Sometimes models as specified by researchers have multiple equilibria. This might be a problem if we want to use the model to forecast the future (as is the case with DSGE models) since we do not know in which equilibrium we will end up. One way to solve this problem is to say that, well, since the model admits several equilibria it means that the model is not fully specified, that is, it is not "closed." Thus, one can propose a condition/conditions to "close" such model so that it has only a single equilibrium.