Synchronization of chaotic nonlinear oscillators: study of two coupled CSTRs

Abashar, M.E.E.; Judd, M.R.

doi:10.1016/s0009-2509(98)00140-7

Cited by 6 publications

(2 citation statements)

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“…the first two representing the dimensionless concentrations Y and Z of reactants A and B (and their conversions into their products). The third equation represents the reactor temperature T. The time series of the latter are used in this analysis, in reference to the accessibility of measurements in real autocatalytic reactors [33,38]. For arbitrary values of β 2 and Da 1 , with α = 250, β 1 = 0.04, γ 1 = γ 2 = 25 and Da 2 = 2.75, the differential equations provide one unique solution to the system's steady-state [39].…”

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confidence: 99%

Recurrence Rate spectrograms for the classification of nonlinear and noisy signals

Hertrampf,

Oberst

2024

Phys. Scr.

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Time series analysis of real-world measurements is fundamental in naturalsciences and engineering, and machine learning has been recently of great assistance especiallyfor classification of signals and their understanding. Yet, the underlying system’s nonlinearresponse behaviour is often neglected. Recurrence Plot (RP) based Fourier-spectra constructedthrough τ-Recurrence Rate (RRτ) have shown the potential to reveal nonlinear traits otherwisehidden from conventional data processing. We report a so far disregarded eligibility forsignal classification of nonlinear time series by training RESnet-50 on spectrogram images,which allows recurrence-spectra to outcompete conventional Fourier analysis. To exemplify itsfunctioning, we employ a simple nonlinear physical flow of a continuous stirred tank reactor,able to exhibit exothermic, first order, irreversible, cubic autocatalytic chemical reactions, anda plethora of fast-slow dynamics. For dynamics with noise being ten times stronger than thesignal, the classification accuracy was up to ≈75 % compared to ≈17 % for the periodogram.We show that an increase in entropy only detected by the RRτ allows differentiation. Thisshows that RP power spectra, combined with off-the-shelf machine learning techniques, havethe potential to significantly improve the detection of nonlinear and noise contaminated signals.

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Section: = --mentioning

confidence: 99%

Recurrence Rate spectrograms for the classification of nonlinear and noisy signals

Hertrampf,

Oberst

2024

Phys. Scr.

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“…Behavioral patterns of two coupled chemical reactors have been studied substantially, with the focus being on the study of chaotic dynamics, quasiperiodicity, and resonance phenomena resulting from the coupling of oscillators and synchronization of these. − This system can be viewed as an aggregation of two subsystems, the individual CSTRs, and displays the phenomenon of emergence featured by complexity theory. Emergence, in this sense, refers to any situation in which a system displays a level of functionality that is not possible for any of its subsystems when considered on their own.…”

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confidence: 99%

Effect of Spatial Segregation on Commensalistic Cultures—Series Reactors

Parulekar

2011

Ind. Eng. Chem. Res.

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A comprehensive analysis of static and dynamic behavior of a mixed culture in two bioreactors in series is presented considering anaerobic digestion involving acidogens (X) and methanogens (Y) as the example bioprocess. A single continuous culture may operate at up to seven steady states, including up to four coexistence steady states, with only one coexistence steady state being locally stable. The bioreactors in the two-reactor system are identical in terms of composition of and dilution rate with respect to fresh feed. A two-reactor system may admit up to forty nine steady states, which are comprised of up to forty coexistence steady states, at least at very low interaction rates (R). When physically realizable, up to five coexistence steady states are locally stable. The static and dynamic analysis of the two-reactor system is facilitated by appropriate grouping of large number of steady states arising for very low R into nine clusters and grouping of the clusters into three cluster groups. Numerical illustrations reveal the rich steady state structure of the bioprocess for bioreactors in series. The two bioreactors can operate at up to five locally stable coexistence steady states over certain ranges of R. The two-reactor system is operationally more flexible and more robust vis-a-vis single reactor as concerns maintenance of mixed culture. Emergence of additional steady states at intermediate R reveals that series bioreactors are an example of a complex system.

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Some Dynamic Features of Fluidised Bed Reactors for Partial Oxidation of o‐Xylene.

Abashar

2003

Dev. Chem. Eng. Mineral Process.

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Synchronization of chaotic nonlinear oscillators: study of two coupled CSTRs

Cited by 6 publications

References 0 publications

Recurrence Rate spectrograms for the classification of nonlinear and noisy signals

Recurrence Rate spectrograms for the classification of nonlinear and noisy signals

Effect of Spatial Segregation on Commensalistic Cultures—Series Reactors

Some Dynamic Features of Fluidised Bed Reactors for Partial Oxidation of o‐Xylene.

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