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Feedback control of subcritical Turing instability with zero mode
A A Golovin1, Y Kanevsky, A A Nepomnyashchy
1Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA.
Summary
Global feedback control stabilizes systems with Turing instability using pattern amplitude measurements. This leads to stable localized patterns or traveling waves, crucial for pattern formation studies.
Area of Science:
- Nonlinear dynamics
- Pattern formation
- Control theory
Background:
- Systems with subcritical instabilities can exhibit complex behaviors.
- Turing instability (short-wave instability) is a key mechanism for pattern formation.
- Zero modes can significantly influence system dynamics.
Purpose of the Study:
- Investigate global feedback control for systems with Turing instability and a zero mode.
- Determine if feedback control can stabilize these systems.
- Analyze the resulting stationary and traveling states.
Main Methods:
- Utilized a Ginzburg-Landau equation coupled with a zero mode equation.
- Employed analytical and numerical simulation techniques.
- Implemented feedback control based on maximum pattern amplitude.
Main Results:
- Feedback control successfully stabilized the system.
- Localized unipulse stationary states were formed.
- Traveling solitary waves emerged due to an instability of stationary states.
Conclusions:
- Global feedback control is effective for stabilizing systems with Turing instability and zero modes.
- The transition to traveling waves is governed by the coupling parameter and zero mode damping.
- This control strategy enables the formation of predictable localized structures.
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