Justh, Eric W.Krishnaprasad, Perinkulam S.Basic properties of solutions and a Lyapunov functionalare presented for a complex activator-inhibitor equation witha cubic nonlinearity.Potential applications include control of coupled-oscillator arrays(for quasi-optical power combining and phased-array antennas),and control of MEMS actuator arrays (for micro-positioning small items).<P>(<I>This work to appear in Proc. 1999 American Control Conference.</I>)en-USdistributed parameter systemslinear systemsnonlinear systemsstabilitycoupled oscillatorsLyapunov functionalpattern-forming systemsIntelligent Control SystemsTechnical Report