Delay induced canards in a model of high speed machining

DOI10.1080/14689360902852547zbMath1185.37135OpenAlexW1990139416MaRDI QIDQ3643147

Thomas Erneux, Sue Ann Campbell, Emily F. Stone

Publication date: 10 November 2009

Published in: Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://dipot.ulb.ac.be/dspace/bitstream/2013/98316/1/DynSys09.pdf

zbMATH Keywords

Hopf bifurcationdelay differential equationdelayed feedback

Mathematics Subject Classification ID

Stability for nonlinear problems in mechanics (70K20) Problems involving a system of particles with friction (70F40) Dynamical aspects of symmetries, equivariant bifurcation theory (37G40) Invariant manifolds of functional-differential equations (34K19)

Related Items (12)

À propos de canards (Apropos canards) ⋮ Canard explosion in delay differential equations ⋮ Smooth inertial manifolds for neutral differential equations with small delays ⋮ Bifurcation Analysis of Wilson-Cowan Model with Singular Impulses ⋮ Large spectral gap induced by small delay and its application to reduction ⋮ Canards of Folded Saddle-Node Type I ⋮ Gevrey Asymptotics of Slow Manifolds in Singularly Perturbed Delay Equations ⋮ Anticipation via canards in excitable systems ⋮ Dynamics of a Mathematical Hematopoietic Stem-Cell Population Model ⋮ Complex oscillations in the delayed Fitzhugh-Nagumo equation ⋮ Singular Hopf bifurcation in a differential equation with large state-dependent delay ⋮ Delay-induced switched states in a slow–fast system

Uses Software

• DDE-BIFTOOL
• psSchur
• XPPAUT

Cites Work

• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Inertial and slow manifolds for delay equations with small delays.
• Stability and bifurcation analysis of a nonlinear DDE model for drilling
• Ikeda Hopf bifurcation revisited
• Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation
• NUMERICAL COMPUTATION OF CANARDS
• Simulating, Analyzing, and Animating Dynamical Systems
• Singular Hopf Bifurcation to Relaxation Oscillations. II
• Stability and Bifurcations of Equilibria in a Multiple-Delayed Differential Equation
• Nonlinear models of chatter in drilling processes
• Singular Hopf Bifurcation to Relaxation Oscillations
• Relaxation oscillations including a standard chase on French ducks
• Handbook of Chaos Control
• IMPROVED NUMERICAL FLOQUET MULTIPLIERS
• Relaxation oscillation and canard explosion

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