On the uniqueness of solutions of nonlinear dynamic networks and systems

In this paper it will be shown that for a fairly broad class of nonlinear dynamic networks and systems, that while global passivity does not imply uniqueness, local passivity implies the uniqueness of the time domain solution. Furthermore, sufficient (and in a sense also close to the necessary) conditions will be presented ensuring the uniqueness of the solution for non-Lipshutzian systems. The mathematical conditions are given also in terms of element characteristics and network topology. The results can be generalized for networks containing multiport timevarying and nonlinear elements.