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Delayed feedback induces motion of localized spots in reaction-diffusion systems
Mustapha Tlidi1, Alberto Sonnino, Giorgio Sonnino
1Faculté des Sciences, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Bruxelles, Belgium.
Summary
Localized spots in reaction-diffusion systems exhibit spontaneous motion when controlled by time-delayed feedback. This study characterizes the motion near a critical point using the delayed Swift-Hohenberg equation.
Area of Science:
- Complex systems dynamics
- Nonlinear physics
- Mathematical modeling
Background:
- Reaction-diffusion systems are fundamental to pattern formation.
- Time-delayed feedback control introduces complex dynamics.
- Localized structures (spots) are prevalent in various scientific models.
Purpose of the Study:
- Investigate the formation and dynamics of localized spots in reaction-diffusion systems.
- Analyze the impact of time-delayed feedback control near a critical point.
- Develop a theoretical framework to describe spot motion.
Main Methods:
- Analytical derivation of the delayed Swift-Hohenberg equation from the FitzHugh-Nagumo model.
- Characterization of localized spot motion through analytical computation of velocity and threshold.
- Numerical simulations to validate theoretical predictions.
Main Results:
- The FitzHugh-Nagumo model near a critical point can be described by the delayed Swift-Hohenberg equation.
- Time-delayed feedback induces spontaneous motion of localized spots.
- Analytical expressions for the velocity and motion threshold of localized spots were derived.
Conclusions:
- Time-delayed feedback control is a key mechanism for inducing directed motion in localized structures.
- The delayed Swift-Hohenberg equation provides an effective model for studying these phenomena.
- Theoretical predictions align well with numerical simulations, confirming the model's validity.
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