TITLE

Slow passage through a supercritical Hopf bifurcation: Time-delayed response in the Belousov–Zhabotinsky reaction in a batch reactor

AUTHOR(S)
Strizhak, Peter; Menzinger, Michael
PUB. DATE
December 1996
SOURCE
Journal of Chemical Physics;12/22/1996, Vol. 105 Issue 24, p10905
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
When the control parameter of a dynamical system varies continuously, bifurcation is delayed due to the inertia in the system's response. We study experimentally the time delay of the supercritical Hopf bifurcation that arises from the parametric drift of the oscillating Belousov-Zhabotinsky reaction under batch conditions. The time-dependent oscillation amplitude and period are analyzed using the normal form of the supercritical Hopf bifurcation with a time-dependent control parameter. We show that this approach describes the time evolution of the entire oscillatory domain from high amplitude to vanishing oscillations.
ACCESSION #
9815270

 

Related Articles

  • Bifurcation structures of periodically forced oscillators. Vance, William N.; Ross, John // Chaos;Dec91, Vol. 1 Issue 4, p445 

    Presents a theoretical investigation of bifurcation structures of periodically forced oscillators. Typical bifurcation diagrams for forced oscillators; Small-amplitude forcing; Forced Hopf bifurcation.

  • Hopf bifurcation in chemical kinetics. Nielsen, K.; Hynne, F.; So\rensen, P. Graae // Journal of Chemical Physics;1/15/1991, Vol. 94 Issue 2, p1020 

    We study Hopf bifurcations in chemical reaction systems for their potential use in quantitative experimental analysis of the kinetics of oscillatory reactions. Three models of the Belousov–Zhabotinsky reaction are investigated as examples. For these we have determined and characterized...

  • The self homotopy set of a Hopf-space. Oshima, H // Quarterly Journal of Mathematics;Dec99, Vol. 50 Issue 200, p483 

    Examines the homotopy set of a Hopf space. Admission of CW complex in the Hopf structure through equality of homotopy to the complexes; Introduction of notations; Formation of the theorems.

  • Kinking number and the Hopf index theorem. Low, Robert J. // Journal of Mathematical Physics;Oct93, Vol. 34 Issue 10, p4840 

    The various definitions of kinking number that have been used are examined and compared, and a general definition is proposed. A generalization of Hopf’s index theorem is given.

  • On the relationship between the streamfunction and velocity potential of the Madden-Julian... Chen, Tsing-Chang; Chen, Jau-Ming // Journal of the Atmospheric Sciences;3/1/97, Vol. 54 Issue 5, p679 

    Examines the relationship between the streamfunction and velocity potential of the Madden-Julian oscillation by zonal wavenumber-1 components. Existence of a quarter-cycle difference; Use of a streamfunction budget equation; Significance of the counteraction between streamfunction tendencies...

  • Six-hour zonally symmetric tidal oscillations of the mesopause over South Pole Station. Sivjee, G.G.; Walterscheid, R.L. // Antarctic Journal of the United States;1993, Vol. 28 Issue 5, p325 

    Investigates the simultaneous observation of a six-hour zonally symmetric tidal oscillations of the mesopause over South Pole Station. Corrections for variations in the spectral sensitivity of the Michelson interferometer (MI); Conversion of the detector signal to optical brightness.

  • Rectification of the Madden--Julian Oscillation into the ENSO Cycle. Kessler, William S.; Kleeman, Richard // Journal of Climate;10/15/2000, Vol. 13 Issue 20, p1 

    An ocean general circulation model, forced with idealized, purely oscillating wind stresses over the western equatorial Pacific similar to those observed during the Madden--Julian oscillation (MJO), developed rectified low-frequency anomalies in SST and zonal currents, compared to a run in...

  • Sun appears to be oscillating at many frequencies.  // Physics Today;May76, Vol. 29 Issue 5, p17 

    Reports the discovery of variations in the frequency of Sun's oscillations. Details on the frequencies; Significance of the discovery; Measurement of the oscillations.

  • Localized excitations in a vertically vibrated granular layer. Umbanhowar, Paul B.; Melo, Francisco // Nature;8/29/1996, Vol. 382 Issue 6594, p793 

    Reports the observation of stable, two-dimensional localized excitations in a vibrating layer of sand. Oscillons as the name given to these excitations; Their propensity to assembling into so-called molecular and crystalline structures; What the experimental results indicate.

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics