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A Lyapunov Functional for the Cubic Nonlinearity Activator-Inhibitor Model Equation
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 ...
Analysis of a complex activator-inhibitor equation
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 ...
Control of Large Actuator Arrays Using Pattern-Forming Systems
Pattern-forming systems are used to model many diverse phenomena from biology,chemistry and physics. These systems of differential equations havethe property that as a bifurcation (or control) parameter passes through ...