We show that two networks of coupled dynamical systems are dynamically equivalent if and only if they are output equivalent. We also obtain necessary and sufficient conditions for two dynamically equivalent networks to be input equivalent. These results were previously described in the companion paper `Dynamical equivalence of networks of coupled dynamical systems' but only proved there for the case of asymmetric inputs. In this paper, we allow for symmetric inputs. We also provide a number of examples to illustrate the main results in the case when there are both symmetric and asymmetric inputs.

For preprint, e-mail: mikefield@gmail.com or Michael.J.Field@rice.edu

Professor Mike Field
Department of Mathematics
Rice University
6100 S Main St
TX 77005-1892