DOUBLE-HOPF BIFURCATION IN AN OSCILLATOR WITH EXTERNAL FORCING AND TIME-DELAYED FEEDBACK CONTROL

DOI10.1142/S0218127406016963zbMath1115.70015MaRDI QIDQ5297807

Pei Yu, Z. Chen

Publication date: 13 July 2007

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

quasi-periodic motionsmultiple-time scalesfour-dimensional center manifold

Mathematics Subject Classification ID

Feedback control (93B52) Forced motions for nonlinear problems in mechanics (70K40) Bifurcations and instability for nonlinear problems in mechanics (70K50) Control of mechanical systems (70Q05) Control/observation systems governed by ordinary differential equations (93C15)

Related Items (4)

Bifurcation Analysis and Chaos Switchover Phenomenon in a Nonlinear Financial System with Delay Feedback ⋮ Hopf and resonant double Hopf bifurcation in congestion control algorithm with heterogeneous delays ⋮ Normal forms of non-resonance and weak resonance double Hopf bifurcation in the retarded functional differential equations and applications ⋮ Periodic and Chaotic Motion of a Time-Delayed Nonlinear System Under Two Coexisting Families of Additive Resonances

Uses Software

• XPPAUT

Cites Work

• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Resonant Hopf-Hopf interactions in delay differential equations
• Limit cycles, tori, and complex dynamics in a second-order differential equation with delayed negative feedback
• Dynamics of a limit cycle oscillator under time delayed linear and nonlinear feedbacks
• Analysis on double Hopf bifurcation using computer algebra with the aid of multiple scales
• Study of double Hopf bifurcation and chaos for an oscillator with time delayed feedback
• COMPUTATION OF NORMAL FORMS VIA A PERTURBATION TECHNIQUE
• Simulating, Analyzing, and Animating Dynamical Systems
• Periodic Solutions of Volterra’s Population Equation with Hereditary Effects
• Stability and Bifurcations of Equilibria in a Multiple-Delayed Differential Equation
• DELAY-INDUCED BIFURCATIONS IN A NONAUTONOMOUS SYSTEM WITH DELAYED VELOCITY FEEDBACKS
• LOCAL STABILITY, HOPF AND RESONANT CODIMENSION-TWO BIFURCATION IN A HARMONIC OSCILLATOR WITH TWO TIME DELAYS

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