Eliminating restrictions of time-delayed feedback control using equivariance

DOI10.3934/DCDS.2016.36.451zbMath1317.34148OpenAlexW2554009120MaRDI QIDQ2515689

Matthias Bosewitz, Isabelle Schneider

Publication date: 6 August 2015

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2016.36.451

zbMATH Keywords

coupled oscillatorsnetworksequivariant Hopf bifurcationspatio-temporal patternstime-delayed feedbackPyragas controlpattern-selective

Mathematics Subject Classification ID

Stability theory of functional-differential equations (34K20) Stabilization of solutions to ordinary differential equations (34H15)

Related Items (9)

Restrictions to the use of time-delayed feedback control in symmetric settings ⋮ Characteristic matrix functions for delay differential equations with symmetry ⋮ Equivariant Pyragas Control of Discrete Waves ⋮ Noninvasive Stabilization of Periodic Orbits in O4-Symmetrically Coupled Systems Near a Hopf Bifurcation Point ⋮ State-dependent act-and-wait time-delayed feedback control algorithm ⋮ Coexistence of infinitely many large, stable, rapidly oscillating periodic solutions in time-delayed Duffing oscillators ⋮ Fokker-Planck equations for time-delayed systems via Markovian embedding ⋮ Geometric invariance of determining and resonating centers: Odd- and any-number limitations of Pyragas control ⋮ Pattern-selective feedback stabilization of Ginzburg-Landau spiral waves

Cites Work

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• Global bifurcation of periodic solutions with symmetry
• Singularities and groups in bifurcation theory. Volume II
• The symmetry perspective. From equilibrium to chaos in phase space and physical space
• Delay equations. Functional-, complex-, and nonlinear analysis
• Feedback control of unstable periodic orbits in equivariant Hopf bifurcation problems
• Delayed feedback control of three diffusively coupled Stuart–Landau oscillators: a case study in equivariant Hopf bifurcation
• Delay stabilization of periodic orbits in coupled oscillator systems

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