Morphisms and currents in infinite nonlinear resistive networks

In this paper we develop a theory of nonlinear resistive infinite electrical networks in the framework of modular sequence spaces. After introducing the notion of network morphism, we show that currents in infinite networks can be approximated by currents in suitable finite networks. Rayleigh monotonicity law for nonlinear networks is studied in detail. Parabolic and hyperbolic networks are introduced and characterized in analogy to the linear case.