Class of nonlinear lossless dynamical systems

There is an intimate relation between certain autonomous nonlinear dynamical systems and numerical algorithms for computing eigenvalues. One of these systems is the Toda lattice, a one-dimensional mechanical model consisting of mass points connected by springs with exponential characteristics. The equilibrium of a transformed version of the equations of motion is equal to the eigen-values of a real symmetric tridiagonal matrix, the entries of which have been used to initialize the dynamical system. Clearly, a nonlinear dynamical electrical network can be modelled on these equations of motion. In this paper several network models are developed, each with individual advantages. For the electrical model matrices with arbitrary sub- and superdiagonal entries are allowed as initial values as opposed to the mechanical one with positive entries only. The losslessness and reciprocity of the electrical Toda lattice can be proved by means of Telegen's Theorem.