Time-delayed feedback control of unstable periodic orbits near a subcritical Hopf bifurcation

DOI10.1016/j.physd.2010.12.011zbMath1219.37062arXiv1006.3479OpenAlexW1988391422MaRDI QIDQ532380

Genevieve C. Brown, Mary Silber, Claire M. Postlethwaite

Publication date: 4 May 2011

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1006.3479

zbMATH Keywords

delay differential equationssubcritical Hopf bifurcationdegenerate Hopf bifurcationtime-delayed feedbackPyragas control

Mathematics Subject Classification ID

Feedback control (93B52) Stabilization of systems by feedback (93D15) Dynamical systems in control (37N35) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (12)

Existence of finite time blow-up solutions in a normal form of the subcritical Hopf bifurcation with time-delayed feedback for small initial functions ⋮ Stabilization of periodic orbits near a subcritical Hopf bifurcation in delay-coupled networks ⋮ Delayed feedback control of a delay equation at Hopf bifurcation ⋮ Restrictions to the use of time-delayed feedback control in symmetric settings ⋮ Resonance Phenomena in a Scalar Delay Differential Equation with Two State-Dependent Delays ⋮ Noninvasive Stabilization of Periodic Orbits in O4-Symmetrically Coupled Systems Near a Hopf Bifurcation Point ⋮ Delay feedback control of the Lorenz-like system ⋮ CONTROL OF SYNCHRONIZATION IN DELAY-COUPLED NETWORKS ⋮ Time-delayed feedback control of unstable periodic orbits near a subcritical Hopf bifurcation ⋮ A degenerate Hopf bifurcation in retarded functional differential equations, and applications to endemic bubbles ⋮ Self-induced synchronization by large delay ⋮ Delay can stabilize: love affairs dynamics

Uses Software

• DDE-BIFTOOL

Cites Work

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• Time-delayed feedback control of unstable periodic orbits near a subcritical Hopf bifurcation
• Order reduction of retarded nonlinear systems - the method of multiple scales versus center-manifold reduction
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Singularities and groups in bifurcation theory. Volume I
• Singularities and groups in bifurcation theory. Volume II
• Introduction to functional differential equations
• Bifurcation, bursting, and spike frequency adaptation
• The Lorenz equations: bifurcations, chaos, and strange attractors
• Introduction to the theory and application of differential equations with deviating arguments. Translated from the Russian by John L. Casti
• Stability and bifurcation analysis of a nonlinear DDE model for drilling
• Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation
• On analytical properties of delayed feedback control of chaos.
• Hopf bifurcation calculations in delayed systems with translational symmetry
• Spatial and temporal feedback control of traveling wave solutions of the two-dimensional complex Ginzburg-Landau equation
• A Maple program for computing a terms of a center manifold, and element of bifurcations for a class of retarded functional differential equations with Hopf singularity
• Traffic jams: dynamics and control
• Delay Differential Equations
• Zero singularities of codimension two and three in delay differential equations
• Stabilization of Long-Period Periodic Orbits Using Time-Delayed Feedback Control
• Bifurcation analysis of an inverted pendulum with delayed feedback control near a triple-zero eigenvalue singularity
• Controlling chaos
• Feedback control of travelling wave solutions of the complex Ginzburg–Landau equation
• Delayed feedback control of chaos
• Handbook of Chaos Control
• Functional differential equations
• Subcritical Hopf bifurcation in the delay equation model for machine tool vibrations

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