Monotonicity in nonlinear resistive circuits

A criterion for the monotonicity of the transfer characteristic from a voltage or current source to a resistor voltage or current in a nonlinear resistive reciprocal or nonreciprocal circuit is given. It assures monotonicity independently of the circuit parameters. Combined with earlier results on the existence and uniqueness of the solution, the criterion becomes purely topological in nature. The method can be generalized to different transfer and driving-point characteristics and to the dependence on circuit parameters. A simple example is given to illustrate the criterion