Convergence analysis of a class of networks of nonlinear coupled oscillators

A network of nonlinear coupled oscillators is presented, and physical motivation is given for the network structure. Next, a rigorous proof of convergence using Lyapunov theory and LaSalle's Invariance Principle is presented, which shows that each trajectory of the network converges to an equilibrium point. Two important generalizations of the network architecture for which the convergence properties are retained are then indicated. Finally, an example is presented to illustrate how such networks could be used, and to indicate how undesired stable equilibria might be dealt with.