Nonexistence of Oscillations in a Nonlinear Distributed Network

摘要

A flip-flop circuit with one equilibrium point is formulated as a transmission line with a nonlinear current-voltage relation at one point. The mathematical model representing this network is a nonlinear functional differential equation of the neutral type. A theorem is proven exploiting the theory of Cruz and Hale for neutral equations which gives conditions for nonexistence of oscillations in the network. The theorem is also shown to validate a type of Aizerman conjecture for the type of nonlinear current-voltage relation. (Author)