Bogdanov–Takens and Triple Zero Bifurcations of Coupled van der Pol–Duffing Oscillators with Multiple Delays

DOI10.1142/S0218127417501334zbMath1373.34108MaRDI QIDQ5371168

Xia Liu, Tonghua Zhang

Publication date: 25 October 2017

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

zbMATH Keywords

time delayoscillatornormal formBogdanov-Takens bifurcationtriple zero bifurcation

Mathematics Subject Classification ID

Transformation and reduction of functional-differential equations and systems, normal forms (34K17) Periodic solutions to functional-differential equations (34K13) Bifurcation theory of functional-differential equations (34K18) Stationary solutions of functional-differential equations (34K21)

Related Items (1)

Dynamical analysis of a competition and cooperation system with multiple delays

Uses Software

• DDE-BIFTOOL

Cites Work

• Unnamed Item
• Unnamed Item
• Bogdanov-Takens bifurcation in a tri-neuron BAM neural network model with multiple delays
• Bogdanov-Takens singularity in Van der Pol's oscillator with delayed feedback
• Inverted pendulum stabilization: characterization of codimension-three triple zero bifurcation via multiple delayed proportional gains
• Bogdanov-Takens bifurcation in an oscillator with negative damping and delayed position feedback
• Normal forms for retarded functional differential equations and applications to Bogdanov-Takens singularity
• Triple-zero bifurcation in van der Pol's oscillator with delayed feedback
• The bifurcation study of 1:2 resonance in a delayed system of two coupled neurons
• Bogdanov-Takens bifurcation in an oscillator with positive damping and multiple delays
• Stability and bifurcation analysis of delay coupled Van der Pol-Duffing oscillators
• Homoclinic orbits and Hopf bifurcations in delay differential systems with T-B singularity
• Zero singularities of codimension two and three in delay differential equations
• Bifurcation analysis of an inverted pendulum with delayed feedback control near a triple-zero eigenvalue singularity
• SOME RESULTS ON CHUA'S EQUATION NEAR A TRIPLE-ZERO LINEAR DEGENERACY
• A NOTE ON THE TRIPLE-ZERO LINEAR DEGENERACY: NORMAL FORMS, DYNAMICAL AND BIFURCATION BEHAVIORS OF AN UNFOLDING
• Bogdanov–Takens and triple zero bifurcations in general differential systems with m delays
• Delay-Induced Double Hopf Bifurcations in a System of Two Delay-Coupled van der Pol–Duffing Oscillators
• Elements of applied bifurcation theory

This page was built for publication: Bogdanov–Takens and Triple Zero Bifurcations of Coupled van der Pol–Duffing Oscillators with Multiple Delays