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The cubic nonlinearity activator-inhibitor model equation is a simpleexample of a pattern-forming system for which strong mathematical resultscan be obtained. Basic properties of solutions and the derivation ofa Lyapunov ...

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 ...

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 ...

A conventional Zernike filter measures wavefront phase by superimposing the aberrated input beam with a phase-shifted version of its zero-orderspectral component. The Fourier-domain phase-shifting is performed by afixed ...

This paper presents a Lie group setting for the problem of control of formations, as a natural outcome of the analysis of a planar two-vehicle formation control law. <p>The vehicle trajectories are described using planar ...

A class of feedback systems for high-resolution optical wave-front control(or adaptive optic wave-front distortion suppression) is modeled andanalyzed. Under certain conditions, the nonlinear dynamical system modelsobtained ...

We consider the formulation and analysis of a problem of automaticcontrol: correcting for the distortion induced in an optical wave frontdue to propagation through a turbulent atmosphere. It has recentlybeen demonstrated ...