Periodic perturbations of an oscillatory chemical system

Gregory Markman, Kedma Bar-Eli

Research output: Contribution to journalArticlepeer-review


The Oregonator model in a continuously stirred tank reactor has been subjected to periodic modulation of the input and output flows of materials. Two cases has been investigated. In both cases the system has three steady states (one of which is always a saddle). In the first case, two steady states are stable. Transitions from one steady state to the other via the perturbations are investigated. In the second case oscillations occur, but they end via saddle-loop bifurcation. Small harmonic oscillations occur if the modulation spans only the stable steady state. When modulation period and amplitude are such that the modulated flow stays partly in the stable region and partly in the unstable region, the oscillations become synchronized with the modulation period. There is a range of modulation amplitude (or period) in which there is a rational ratio between the oscillations period and that of the modulation. Between any two such steps of synchronization there is always another step in which the period is the sum of the two periods, and the pattern is a combination of the patterns on its two sides. As the period increases its step size decreases. A simple power relationship exists between the step size and its period. These synchronized oscillations are always periodic, and no period doubling or chaotic oscillations have been observed.

Original languageEnglish
Pages (from-to)12248-12254
Number of pages7
JournalJournal of Physical Chemistry
Issue number47
StatePublished - 1994


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