Delayed feedback control of three diffusively coupled Stuart–Landau oscillators: a case study in equivariant Hopf bifurcation | Zendy

I. Schneider | Zendy

Open Access

Delayed feedback control of three diffusively coupled Stuart–Landau oscillators: a case study in equivariant Hopf bifurcation

Author(s) -

I. Schneider

Publication year - 2013

Publication title -

philosophical transactions of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.074

H-Index - 169

eISSN - 1471-2962

pISSN - 1364-503X

DOI - 10.1098/rsta.2012.0472

Subject(s) - equivariant map , hopf bifurcation , bifurcation , mathematics , control theory (sociology) , physics , feedback control , control (management) , classical mechanics , statistical physics , quantum mechanics , computer science , pure mathematics , nonlinear system , artificial intelligence , engineering , control engineering

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.

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