TWO-TO-ONE RESONANT HOPF BIFURCATIONS IN A QUADRATICALLY NONLINEAR OSCILLATOR INVOLVING TIME DELAY

DOI10.1142/S0218127412500605zbMath1270.34186MaRDI QIDQ2843551

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Publication date: 23 August 2013

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

zbMATH Keywords

time delayfeedback controlnonlinear oscillatorquadratic nonlinearitiesHopf-Hopf interactionsresonant Hopf bifurcationstwo-to-one internal resonances

Mathematics Subject Classification ID

Feedback control (93B52) Transformation and reduction of functional-differential equations and systems, normal forms (34K17) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Qualitative investigation and simulation of models involving functional-differential equations (34K60) Bifurcation theory of functional-differential equations (34K18) Invariant manifolds of functional-differential equations (34K19)

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Cites Work

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• Stability and dynamics of a controlled van der Pol-Duffing oscillator
• Stability and Hopf bifurcation of the maglev system with delayed position and speed feedback control
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Resonant Hopf-Hopf interactions in delay differential equations
• A theoretical and experimental implementation of a control method based on saturation
• Stability and bifurcation analysis in Van der Pol's oscillator with delayed feedback
• Nonresonant Hopf bifurcations of a controlled van der Pol–Duffing oscillator
• LOCAL HOPF BIFURCATION OF COMPLEX NONLINEAR SYSTEMS WITH TIME-DELAY
• The nonresonant double Hopf bifurcation in delayed neural network

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