Resonance and Bifurcation of Higher-dimensional Tori
نویسنده
چکیده
By means of an example it is shown that a supercritical bifurcation of an invariant 2-torus into an invariant 3-torus prevailing in the case of nonresonance may be replaced by a transcritical bifurcation into a pinched invariant 3-torus in the case of resonance. The connections of these bifurcation phenomena with the properties of the spectrum of the underlying invariant 2-torus are discussed. 1. Statement of the results. 1.
منابع مشابه
Post-critical Behavior of Three- dimensional Composite Beams Near the Autoparametric Resonance under Flapwise Excitation
The bifurcation analysis of a composite beam subjected to harmonic flapwise base excitation is studied when the ratio of flapwise and chordwise internal resonances is 1:2. Results are obtained by the numerical solution of modulation equations. Chracteristics of the response are investigated in terms of time history, phase portraits diagrams and bifurcation diagram of poincare maps. It is observ...
متن کاملTopological Compression Factors of 2-Dimensional TUC4C8(R) Lattices and Tori
We derived explicit formulae for the eccentric connectivity index and Wiener index of 2-dimensional square-octagonal TUC4C8(R) lattices with open and closed ends. New compression factors for both indices are also computed in the limit N-->∞.
متن کاملOn the Hopf-Pitchfork bifurcation in the Chua's equation
We study some periodic and quasiperiodic behaviors exhibited by the Chua’s equation with a cubic nonlinearity, near a Hopf–pitchfork bifurcation. We classify the types of this bifurcation in the nondegenerate cases, and point out the presence of a degenerate Hopf–pitchfork bifurcation. In this degenerate situation, analytical and numerical study shows a diversity of bifurcations of periodic orb...
متن کاملA periodically forced flow displaying symmetry breaking via a three-tori gluing bifurcation and two-tori resonances
The dynamics due to a periodic forcing (harmonic axial oscillations) in a Taylor–Couette apparatus of finite length is examined numerically in an axisymmetric subspace. The forcing delays the onset of centrifugal instability and introduces a Z2 symmetry that involves both space and time. This paper examines the influence of this symmetry on the subsequent bifurcations and route to chaos in a on...
متن کاملFolding tori and Chenciner bubbles in an ENSO model with delayed feedback
We consider the sudden disappearance of stable invariant tori in a delay differential equation (DDE) model of the coupled El Niño Southern Oscillation (ENSO) system. This phenomenon can be explained by the folding of invariant tori and their resonance tongues, which are associated with bifurcation structures referred to as Chenciner bubbles. We identify and analyse a Chenciner bubble and show h...
متن کامل