THE NONLINEAR PERRON-FROBENIUS THEOREM - PERTURBATIONS AND AGGREGATION

The dominant eigenvalue and the corresponding eigenvector (or Perron v ector) of a non-linear eigensystem are considered. We discuss the effe cts upon these, of perturbations and of aggregation of the underlying mapping. The results are applied to study the sensivity of the outputs in a non-linear input-output model. For that purpose, it is shown tha t the input-output model can be rewritten as a non-linear eigensystem. It turns out that the Perron vector of this eigensystem includes the solution vector of the input-output model.