Related Experiment Video
Updated: Feb 2, 2026

Movement Retraining using Real-time Feedback of Performance
Published on: January 17, 2013
Stationary localized structures and the effect of the delayed feedback in the Brusselator model
Abstract:
The Brusselator reaction-diffusion model is a paradigm for the understanding of dissipative structures in systems out of equilibrium. In the first part of this paper, we investigate the formation of stationary localized structures in the Brusselator model. By using numerical continuation methods in two spatial dimensions, we establish a bifurcation diagram showing the emergence of localized spots. We characterize the transition from a single spot to an extended pattern in the form of squares. In the second part, we incorporate delayed feedback control and show that delayed feedback can induce a spontaneous motion of both localized and periodic dissipative structures. We characterize this motion by estimating the threshold and the velocity of the moving dissipative structures.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)'.
Related Concept Videos
Feedback Inhibition
Feedback Loops
Local Anesthetics: Chemistry and Structure-Activity Relationship
Effects of feedback
Feedback significantly modifies the gain of a control system. The gain of a system without feedback is altered by a factor of one plus GH, where G represents...
Feedback control systems
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
Facial Feedback Hypothesis

