Stability of mode locked states of coupled oscillator arrays

Author

Lynch, Jonathan J. ; York, Robert A.

Author_Institution

Dept. of Electr. Eng., California Univ., Santa Barbara, CA, USA

Volume

42

Issue

8

fYear

1995

fDate

8/1/1995 12:00:00 AM

Firstpage

413

Lastpage

418

Abstract

A method for analyzing beat frequency entrained (or mode locked) systems of coupled nonlinear oscillators is presented. Stable mode locked states are almost periodic oscillations that occur outside of the fundamental entrainment region of the array, and generate a periodic pulse train when the oscillator outputs are summed. The analysis relates the stability of the states to the relationship between the frequency pullings and the time average phases of the oscillators. The method is applied to three mode locked Van der Pol oscillators with arbitrary coupling time delay, and shows that the mode locking bandwidth is maximized for specific values of coupling delay and oscillator nonlinearity parameter

Keywords

circuit stability; coupled circuits; delays; millimetre wave oscillators; nonlinear network analysis; relaxation oscillators; Van der Pol oscillators; almost periodic oscillations; coupled oscillator arrays; coupling delay; frequency pullings; mode locked states; mode locking bandwidth; nonlinear oscillators; oscillator nonlinearity parameter; periodic pulse train; stability; three mode locked oscillators; time average phases; Couplings; Delay effects; Equations; Frequency; Laser mode locking; Microwave oscillators; Millimeter wave technology; Stability analysis; Steady-state; Transmitters;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.404045

Filename

404045