  In this work, we introduce and study a class of Deep Neural Networks (DNNs)
in continuous-time. The proposed architecture stems from the combination of
Neural Ordinary Differential Equations (Neural ODEs) with the model structure
of recently introduced Recurrent Equilibrium Networks (RENs). We show how to
endow our proposed NodeRENs with contractivity and dissipativity -- crucial
properties for robust learning and control. Most importantly, as for RENs, we
derive parametrizations of contractive and dissipative NodeRENs which are
unconstrained, hence enabling their learning for a large number of parameters.
We validate the properties of NodeRENs, including the possibility of handling
irregularly sampled data, in a case study in nonlinear system identification.
