论文信息 - Resonance Surfaces for Forced Oscillators

Resonance Surfaces for Forced Oscillators

The study of resonances in systemssuch as periodically forced oscillators has traditionally focused on understanding the regions in the parameter plane where these resonances occur. Resonance regions can also be viewed as projections to the parameter plane of resonance surfaces in the four-dimensional Cartesian product of the state space with the parameter space. This paper reports on a computer study of resonance surfaces for a particular family and illustrates some advantages of viewing resonance regions in this light.

Richard McGehee | Bruce B. Peckham

[1] Bruce B. Peckham,et al. Period doubling with higher-order degeneracies , 1991 .

[2] Milos Dolnik,et al. Resonance behaviour in two-parameter families of periodically forced oscillators , 1988 .

[3] Alain Chenciner,et al. Bifurcations de points fixes elliptiques. II. Orbites periodiques et ensembles de Cantor invariants , 1985 .

[4] J. Ross,et al. A detailed study of a forced chemical oscillator: Arnol'd tongues and bifurcation sets , 1989 .

[5] Vladimir Igorevich Arnold,et al. Geometrical Methods in the Theory of Ordinary Differential Equations , 1983 .

[6] Aronson,et al. Entrainment regions for periodically forced oscillators. , 1986, Physical review. A, General physics.

[7] Glen R. Hall,et al. Resonance Zones in Two-Parameter Families of Circle Homeomorphisms , 1984 .

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

[9] K. Tomita,et al. Stroboscopic Phase Portrait of a Forced Nonlinear Oscillator , 1979 .

[10] Raymond A. Adomaitis,et al. RESONANCE PHENOMENA IN AN ADAPTIVELY-CONTROLLED SYSTEM , 1991 .

[11] I. Kevrekidis,et al. The stirred tank forced , 1986 .

[12] Bruce B. Peckham,et al. The necessity of the Hopf bifurcation for periodically forced oscillators , 1990 .

[13] D. Aronson,et al. Bifurcations from an invariant circle for two-parameter families of maps of the plane: A computer-assisted study , 1982 .