论文信息 - Hopf bifurcation formula for first order differential-delay equations

Hopf bifurcation formula for first order differential-delay equations

Abstract This work presents an explicit formula for determining the radius of a limit cycle which is born in a Hopf bifurcation in a class of first order constant coefficient differential-delay equations. The derivation is accomplished using Lindstedt’s perturbation method.

Richard H. Rand | Anael Verdugo | R. Rand | A. Verdugo

[1] B. Hassard,et al. Theory and applications of Hopf bifurcation , 1981 .

[2] M. Freedman,et al. A Poincaré-Lindstedt approach to bifurcation problems for differential-delay equations , 1980 .

[3] Tamás Kalmár-Nagy,et al. Subcritical Hopf Bifurcation in the Delay Equation Model for Machine Tool Vibrations , 2001 .

[4] G. Stépán. Retarded dynamical systems : stability and characteristic functions , 1989 .

[5] D. Armbruster,et al. "Perturbation Methods, Bifurcation Theory and Computer Algebra" , 1987 .

[6] Sue Ann Campbell,et al. Complex dynamics and multistability in a damped harmonic oscillator with delayed negative feedback. , 1995, Chaos.

[7] P. Holmes,et al. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.