Double Hopf bifurcation and quasi-periodic attractors in delay-coupled limit cycle oscillators

DOI10.1016/j.jmaa.2011.10.023zbMath1244.34095OpenAlexW2007074079MaRDI QIDQ655514

Hongbin Wang, Weihua Jiang, Yanqiu Li

Publication date: 4 January 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.10.023

zbMATH Keywords

quasi-periodic solutiondouble Hopf bifurcationthree-dimensional tours

Mathematics Subject Classification ID

Transformation and reduction of functional-differential equations and systems, normal forms (34K17) Almost and pseudo-almost periodic solutions to functional-differential equations (34K14) Periodic solutions to functional-differential equations (34K13) Bifurcation theory of functional-differential equations (34K18) Invariant manifolds of functional-differential equations (34K19)

Related Items (10)

Computation of double Hopf points for delay differential equations ⋮ Hopf Bifurcation and Hidden Attractors of a Delay-Coupled Duffing Oscillator ⋮ Double Hopf bifurcation of coupled dissipative stuart-Landau oscillators with delay ⋮ Double Hopf bifurcation in nonlocal reaction-diffusion systems with spatial average kernel ⋮ Normal form for high-dimensional nonlinear system and its application to a viscoelastic moving belt ⋮ Normal forms of non-resonance and weak resonance double Hopf bifurcation in the retarded functional differential equations and applications ⋮ Double Hopf bifurcation in microbubble oscillators with delay coupling ⋮ Hopf bifurcation control for the main drive delay system of rolling mill ⋮ Hopf-transcritical bifurcation in toxic phytoplankton-zooplankton model with delay ⋮ Delay-Induced Double Hopf Bifurcations in a System of Two Delay-Coupled van der Pol–Duffing Oscillators

Uses Software

• CNN

Cites Work

• Hopf-transcritical bifurcation in retarded functional differential equations
• A theory for synchronization of dynamical systems
• Double delayed feedback control for the stabilization of unstable steady states in chaotic systems
• Oscillator death in coupled functional differential equations near Hopf bifurcation
• Bogdanov-Takens singularity in Van der Pol's oscillator with delayed feedback
• Stability switches and Hopf bifurcations in a pair of delay-coupled oscillators
• Amplitude response of coupled oscillators
• Stability and bifurcation analysis in an amplitude equation with delayed feedback
• Double Hopf bifurcation with strong resonances in delayed systems with nonlinearities
• Hopf-pitchfork bifurcation in van der Pol's oscillator with nonlinear delayed feedback
• Computation of the simplest normal form of a resonant double Hopf bifurcation system with the complex normal form method
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Theory of functional differential equations. 2nd ed
• Elements of applied bifurcation theory.
• Total and partial amplitude death in networks of diffusively coupled oscillators
• Bifurcation analysis in a limit cycle oscillator with delayed feedback
• Time delay effects on coupled limit cycle oscillators at Hopf bifurcation
• Normal forms for retarded functional differential equations and applications to Bogdanov-Takens singularity
• Double Hopf bifurcations and chaos of a nonlinear vibration system
• Two-parameter bifurcations in a network of two neurons with multiple delays
• Double Hopf bifurcation for van der Pol-Duffing oscillator with parametric delay feedback control
• The nonresonant double Hopf bifurcation in delayed neural network
• Coordination of groups of mobile autonomous agents using nearest neighbor rules
• Stability analysis of swarms
• Consensus Problems in Networks of Agents With Switching Topology and Time-Delays
• Emergent Behavior in Flocks
• An Efficient Method for Studying Weak Resonant Double Hopf Bifurcation in Nonlinear Systems with Delayed Feedbacks
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Double Hopf bifurcation and quasi-periodic attractors in delay-coupled limit cycle oscillators