Related Experiment Video
Updated: May 8, 2026

A Microfluidics Approach for the Functional Investigation of Signaling Oscillations Governing Somitogenesis
Published on: March 19, 2021
Delayed feedback control of three diffusively coupled Stuart-Landau oscillators: a case study in equivariant Hopf
1Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, 14195 Berlin, Germany. isabelle.schneider@fu-berlin.de
Abstract:
The modest aim of this case study is the non-invasive and pattern-selective stabilization of discrete rotating waves ('ponies on a merry-go-round') in a triangle of diffusively coupled Stuart-Landau oscillators. We work in a setting of symmetry-breaking equivariant Hopf bifurcation. Stabilization is achieved by delayed feedback control of Pyragas type, adapted to the selected spatio-temporal symmetry pattern. Pyragas controllability depends on the parameters for the diffusion coupling, the complex control amplitude and phase, the uncontrolled super-/sub-criticality of the individual oscillators and their soft/hard spring characteristics. We mathematically derive explicit conditions for Pyragas control to succeed.
Related Concept Videos
Root Loci for Positive-Feedback Systems
The construction rules for the root locus in positive feedback systems are similar to those in...
Damped Oscillations
Although friction and other non-conservative...
BIBO stability of continuous and discrete -time systems
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
Transmission-Line Differential Equations
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from the...
Oscillations In An LC Circuit
Oscillations about an Equilibrium Position
