Depending on the connectivity, recurrent networks of simple computational units can show very different types of dynamics, ranging from totally ordered to chaotic. We analyze how the type of dynamics (ordered or chaotic) exhibited by randomly connected networks of threshold gates driven by a time-varying input signal depends on the parameters describing the distribution of the connectivity matrix. In particular, we calculate the critical boundary in parameter space where the transition from ordered to chaotic dynamics takes place. Employing a recently developed framework for analyzing real-time computations, we show that only near the critical boundary can such networks perform complex computations on time series. Hence, this result strongly supports conjectures that dynamical systems that are capable of doing complex computational tasks should operate near the edge of chaos, that is, the transition from ordered to chaotic dynamics.

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