Chemical oscillations, chaos, and fluctuations in flow reactors

Schneider, F. W.; Muenster, A.

doi:10.1021/j100159a012

Cited by 63 publications

(39 citation statements)

References 4 publications

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“…In the BZ reaction bursting occurs through the presence of an additional secondary Hopf bifurcation which is located at a slightly lower flow-rate. 22 The observed bursts originate from a combination of these two Hopf bifurcations when the perturbation drives the system into the lower flow-rate ranges for a sufficiently long time.…”

Section: Discussionmentioning

confidence: 96%

“…If the time scale of the noise allows resonance of the fluctuations with the focus, relatively small perturbations may lead to large excursions through phase space. 22 In contrast, fluctuations occuring on a very fast time scale do not couple effectively to the system's dynamics, and amplification cannot be observed.…”

Section: Random External Forcing Of the Focal Steady Statementioning

confidence: 99%

See 1 more Smart Citation

Quasiperiodic Forcing of a Chemical Reaction: Experiments and Calculations

Zeyer¹,

Muenster²,

Schneider³

1995

J. Phys. Chem.

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We present experimental and theoretical investigations of the nonlinear resonance behavior of a focal steady state in the Belousov-Zhabotinsky (BZ) reaction which is perturbed by its own dynamics. For this purpose the outputs of two independent BZ-oscillators of incommensurate frequencies are linearly combined in analogy to a simple feed-forward net to achieve the quasiperiodic driving of a third BZ-reactor which is in a focal steady state. For low amplitudes of the quasiperiodic flow-rate perturbations the response is also quasiperiodic in the focal BZ-reactor. Above a threshold value of the quasiperiodic amplitudes, however, single bursts are observed at small phase differences between the two perturbing oscillators. A further increase in the amplitude leads to groups of bursts with small oscillations in between. Aperiodic stochastic bursting in the BZ-reactor is observed when the flow-rate into the focal reactor is perturbed by Gaussian distributed white noise of sufficiently high amplitude and pulse length. The experiments are shown to agree with computer simulations using the Showalter-Noyes-Bar-Eli (SNB) model. At high amplitudes of quasiperiodic forcing the SNBmodel gives evidence for the existence of an attractor which is strange but nonchaotic (information dimension = 2.0).

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Section: Discussionmentioning

confidence: 96%

Section: Random External Forcing Of the Focal Steady Statementioning

confidence: 99%

Quasiperiodic Forcing of a Chemical Reaction: Experiments and Calculations

Zeyer¹,

Muenster²,

Schneider³

1995

J. Phys. Chem.

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“…Deterministic temporal chaos in chemical reaction systems, especially in the Belousov-Zhabotinsky (BZ) reaction, has been well studied in the last 20 years [1][2][3][4][5]; its characteristic behavior has been well understood by the concept of stranger attractor and the methods such as phase portraits of the reconstructed attractors, Poincaré sections, return maps, and generalized Renyi dimensions [6][7][8][9]. A natural extension on this line of research is to understand the spatiotemporal chaos in spatially extended chemical systems, where the embedding dimension of the dynamics is very high and one may expect to observe high-dimensional chaos.…”

Section: Introductionmentioning

confidence: 99%

Chemical waves with line defects in the Belousov-Zhabotinsky reaction

Guo

Wang

et al. 2004

Phys. Rev. E

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We report our experimental observations of line-defected chemical waves in a quasi-two-dimensional reaction-diffusion system of Belousov-Zhabotinsky reaction. The observed line defects are explicit, which can be directly monitored in real time. In the parameter space, the state of the chemical waves with line defects is located between two regimes of the defect-mediated turbulence. The line defects appear in target waves as well as in spiral waves. We demonstrate that the line defects come out in traveling waves as the later reorganize their spatial topologies to adapt to the change in the local dynamics from simple to complex oscillations or vice versa.

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“…Bifurcations of limit cycles (secondary Hopf and period doubling bifurcations) have also been observed. In particular, routes to chaos via period doubling [2] or quasiperiodicity (breakdown of a torus) [3] have been described in a number of publications.…”

Section: Resultsmentioning

confidence: 99%