Convergence Analysis and Analog Circuit Applications for a Class of Networks of Nonlinear Coupled Oscillators

The physical motivation and rigorous proof of convergence for a particular network of nonlinear coupled oscillators are reviewed. Next, the network and convergence proof are generalized in several ways, to make the network more applicable to actual engineering problems. It is argued that such coupled oscillator circuits are more natural to implement in analog hardware than other types of dynamical equations because the signal levels tend to remain at su ciently large values that e ects of o sets and mismatch are minimized. Examples of how analog implementations of these networks are able to address actual control problems are given. The rst example shows how a pair of coupled oscillators can be used to compensate for the feedback path phase shift in a complex LMS loop, and has potential application for analog adaptive antenna arrays or linear predictor circuits. The second example shows how a single oscillator circuit with feedback could be used for continuous wavelet transform applications. Finally, analog CMOS implementation of the coupled oscillator dynamics is brie y discussed. This research was supported in part by the National Science Foundation's Engineering Research Centers Program: NSFD CDR 8803012, and by the AFOSR University Research Initiative Program, under grant AFOSR-90-0105 and AFOSR-F49620-92-J-0500. Also, the authors acknowledge the O ce of Naval Research for their support of this work. Finally, this work was partially supported by a National Science Foundation Graduate Fellowship.