Convergence Analysis of a Class of Networks of Nonlinear Coupled Oscillators

Abstract

A network of nonlinear coupled oscillators is presented, and a convergence proof is given along with physical motivation. Next, the network architecture is generalized by allowing interconnections between oscillators to be controlled in an adaptive fashion, and convergence of the generalized network is proved. An example network is presented to illustrate the utility of such networks and to show why the problem of undesired stable equilibria must be addressed. Two alternative approaches are then presented which overcome the problem of undesired stable equilibria appearing in the network dynamics. Finally, an analog VLSI approach to implementation of such networks is presented, and tradeoffs among power dissipation, bandwidth, and network size are discussed.