Aspects of stable and unstable machining by Hopf bifurcation

DOI10.1016/S0307-904X(02)00052-5zbMath1025.34076MaRDI QIDQ1861698

Mustapha S. Fofana

Publication date: 10 March 2003

Published in: Applied Mathematical Modelling (Search for Journal in Brave)

zbMATH Keywords

stabilityHopf bifurcationdelay differential equationschatter

Mathematics Subject Classification ID

Vibrations in dynamical problems in solid mechanics (74H45) Stability of dynamical problems in solid mechanics (74H55) Dynamical bifurcation of solutions to dynamical problems in solid mechanics (74H60) Bifurcation theory of functional-differential equations (34K18)

Related Items (3)

Illustrative applications of the theory of delay dynamical systems ⋮ Deterministic and stochastic bifurcations of the catalytic CO oxidation on Ir(111) surfaces with multiple delays ⋮ Hopf bifurcation for delay differential equation with application to machine tool chatter

Cites Work

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• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Singularities and groups in bifurcation theory. Volume I
• Classification and unfoldings of degenerate Hopf bifurcations
• Ordinary and delay differential equations
• Introduction to functional differential equations
• Limit cycles, tori, and complex dynamics in a second-order differential equation with delayed negative feedback
• Introduction to the theory and application of differential equations with deviating arguments. Translated from the Russian by John L. Casti
• Delay equations. Functional-, complex-, and nonlinear analysis
• Sources of nonlinearities, chatter generation and suppression in metal cutting
• Stability and Bifurcations of Equilibria in a Multiple-Delayed Differential Equation

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