DOUBLE HOPF BIFURCATION IN DELAYED VAN DER POL–DUFFING EQUATION

DOI10.1142/S0218127413500144zbMath1270.34185MaRDI QIDQ2845328

Weihua Jiang, Pei Yu, Yuting Ding

Publication date: 22 August 2013

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

zbMATH Keywords

normal formmultiple time scalesdouble Hopf bifurcationcenter manifold reductionvan der Pol-Duffing equation

Mathematics Subject Classification ID

Transformation and reduction of functional-differential equations and systems, normal forms (34K17) Qualitative investigation and simulation of models involving functional-differential equations (34K60) Bifurcation theory of functional-differential equations (34K18) Singular perturbations of functional-differential equations (34K26) Invariant manifolds of functional-differential equations (34K19)

Related Items

Bifurcation Analysis and Chaos Switchover Phenomenon in a Nonlinear Financial System with Delay Feedback ⋮ Double Hopf bifurcation of coupled dissipative stuart-Landau oscillators with delay ⋮ Hopf-zero bifurcation in a generalized Gopalsamy neural network model ⋮ Double Hopf bifurcation in a container crane model with delayed position feedback ⋮ Bifurcation phenomena and control analysis in class-B laser system with delayed feedback ⋮ Normal forms of non-resonance and weak resonance double Hopf bifurcation in the retarded functional differential equations and applications ⋮ Equivalence of the MTS Method and CMR Method for Differential Equations Associated with Semisimple Singularity ⋮ Nonlinear interactions between unstable oscillatory modes in a cantilevered pipe conveying fluid ⋮ Hopf-Hopf bifurcation in the delayed nutrient-microorganism model ⋮ Double Hopf bifurcation in microbubble oscillators with delay coupling ⋮ Bifurcation analysis in a delayed toxic-phytoplankton and zooplankton ecosystem with Monod-Haldane functional response ⋮ A method to determine oscillation emergence bifurcation in time-delayed LTI system with single lag ⋮ Delay-Induced Double Hopf Bifurcations in a System of Two Delay-Coupled van der Pol–Duffing Oscillators ⋮ Equivalence of MTS and CMR methods associated with the normal form of Hopf bifurcation for delayed reaction-diffusion equations

Cites Work

• Singular perturbation methods for nonlinear dynamic systems with time delays
• Hopf-transcritical bifurcation in retarded functional differential equations
• Order reduction of retarded nonlinear systems - the method of multiple scales versus center-manifold reduction
• Bogdanov-Takens singularity in Van der Pol's oscillator with delayed feedback
• Hopf-pitchfork bifurcation in van der Pol's oscillator with nonlinear delayed feedback
• Stability and Hopf bifurcation of a class of TCP/AQM networks
• 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
• Effects of time delayed position feedback on a van der Pol-Duffing oscillator
• Multiple scales without center manifold reductions for delay differential equations near Hopf bifurcations
• Normal forms for retarded functional differential equations and applications to Bogdanov-Takens singularity
• Double Hopf bifurcation for van der Pol-Duffing oscillator with parametric delay feedback control
• Bifurcation analysis in van der Pol's oscillator with delayed feedback
• Toroidal normal forms for bifurcations in retarded functional differential equations. I: Multiple Hopf and transcritical/multiple Hopf interaction
• COMPUTATION OF NORMAL FORMS VIA A PERTURBATION TECHNIQUE
• SYMBOLIC COMPUTATION OF NORMAL FORMS FOR RESONANT DOUBLE HOPF BIFURCATIONS USING A PERTURBATION TECHNIQUE
• MULTIPLE BIFURCATION ANALYSIS IN A NEURAL NETWORK MODEL WITH DELAYS
• DELAY-INDUCED BIFURCATIONS IN A NONAUTONOMOUS SYSTEM WITH DELAYED VELOCITY FEEDBACKS
• An Efficient Method for Studying Weak Resonant Double Hopf Bifurcation in Nonlinear Systems with Delayed Feedbacks
• Bifurcation analysis in a scalar delay differential equation