  We consider infinite heterogeneous networks, consisting of input-to-state
stable subsystems of possibly infinite dimension. We show that the network is
input-to-state stable, provided that the gain operator satisfies a certain
small-gain condition. We show that for finite networks of nonlinear systems
this condition is equivalent to the so-called strong small-gain condition of
the gain operator (and thus our results extend available results for finite
networks), and for infinite networks with a linear gain operator they
correspond to the condition that the spectral radius of the gain operator is
less than one. We provide efficient criteria for input-to-state stability of
infinite networks with linear gains, governed by linear and homogeneous gain
operators, respectively.
