Input-out properties of the Toda lattice

This paper establishes a number of inequalities showing that the periodic Toda lattice acts like a self timed shift register for pulses if the initial conditions are appropriately chosen and that this behavior is robust with respect to small changes, noise, and implementation imperfections. We also establish an estimate relating to the progression of pulses in the periodic Toda lattice. These models have solutions that resemble the action potentials observed in neurological signaling.