Analysis of ILM Logic Operations via van der Pol Phase Planes

Logic operations that have previously been numerically demonstrated using intrinsic localized modes (ILMs) in a driven nonlinear 1-D lattice are analyzed using van der Pol phase planes. The time dependent application of a vibrational impurity mode either can produce or destroy an ILM. The appearance or absence of the resulting ILM can be understood via trajectories in the phase plane controlled by the evolving attractors associated with the time dependent impurity mode. Switching between the two possible branches depends on the phase of the amplitude modulation when the impurity mode is removed.