Modelling complex transient oscillations for the BZ reaction in a batch reactor

Johnson, Barry R.; Scott, Stephen K.; Thompson, Barnaby W.

doi:10.1063/1.166254

Cited by 33 publications

(24 citation statements)

References 11 publications

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“…This result is an example of qualitative changes of a dynamical system, which is peculiar to transient dynamics. This type of phenomenon has not been investigated extensively; however, some researchers have reported bifurcation-like phenomena induced by the change of slow parameters [Wang et al, 1994;Johnson et al, 1997;Kang & Tsuda, 2009;Katori et al, 2011]. In addition, Doi et al [Doi et al, 1998] reported bifurcations in the second or subsequent eigenvalues of an operator that describes density evolution in a stochastic dynamical system.…”

Section: Two Coupled Ns Modelsmentioning

confidence: 99%

Numerical Analysis of Transient and Periodic Dynamics in Single and Coupled Nagumo–sato Models

Oku

Aihara

2012

Int. J. Bifurcation Chaos

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The Nagumo–Sato (NS) model is a one-dimensional piecewise linear map that describes simplified dynamics of a single neuron. The NS model and its network extension, coupled Nagumo–Sato models, exhibit complex behavior both in their transient dynamics and after converging to periodic orbits. However, the way the period and the transient length change against the parameters is not completely understood. In this study, we numerically investigate the transient and periodic dynamics in single and coupled NS models. Simulation results indicate the following observations. (1) The period of a single NS model shows layered structures associated with the Farey sequence. (2) Two coupled NS models show discontinuity in the transient length, even though the period does not change. (3) In the case of an associative memory model consisting of NS models, there exists a small parameter region where both the period and the transient length increase considerably. The dynamics within the region is much more complex than that outside the region.

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Section: Two Coupled Ns Modelsmentioning

confidence: 99%

Numerical Analysis of Transient and Periodic Dynamics in Single and Coupled Nagumo–sato Models

Oku

Aihara

2012

Int. J. Bifurcation Chaos

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“…This modelling runs counter to the established method of modelling chemical kinetics in which the generated ordinary differential equations are solved through eigenvalues and eigenvectors. [9][10][11][12] A model of the chemical system which does not utilize kinetics constants may appear to have no relationship with the system under study.…”

Section: Bro3mentioning

confidence: 99%

Lyapunov exponents and the Belousov-Zhabotinsky oscillator: an interactive computational approach

Eskew

Simoyi

2017

S.Afr.j.chem.

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The Belousov-Zhabotinsky (BZ) chemical oscillator is the most studied oscillator. It has been modelled on the basis of single-step mechanisms which have been continuously refined since the seminal manuscript by Field, Koros and Noyes in 1972. This manuscript reports on a unique way of modelling the global dynamics of the oscillator by assuming that the BZ oscillator has shown chaotic behaviour. The unique mathematical definition of chaos is very stringent, and, in this manuscript, we attempt to trace this unique exotic behaviour by the use of 'onto' maps of the interval onto itself which are known to exhaustively show a universal sequence of states that has all the hallmarks of chaotic behaviour. A series of one-humped maps of the interval display, through iterations and subsequent symbolic dynamics, a universal sequence of steps that commence with period-doubling, culminating in chaotic behaviour at some accumulation point of an appropriate bifurcation parameter. We put this theory to the test for the BZ oscillator in this manuscript by selecting a unique continuous map of the interval. This was then decomposed by an iterative treatment. Metric entropy and subsequent arbiter of chaotic behaviour was determined by evaluation of Lyapunov exponents which were then compared to observed BZ oscillator states. Our proposed map satisfactorily modelled the global dynamics of the BZ oscillator; predicted period-doubling, and a regime after a critical bifurcation parameter, where chaotic sequences were dense. We also produce, in the Addendum, an iterative MatLab procedure that any reader can utilize to reveal the type of states and behaviour reported here. KEYWORDS BZ Oscillator, chemical chaos, one-dimensional maps, maps of the interval, symbolic dynamics, Lyapunov characteristic exponent.

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“…The numerous dynamic states such as simple, mixed−mode and chaotic oscillations obtained in BZ reaction system under various experimental conditions [18][19][20][21], can be obtained by numerical simulations using different models. They all have an important role in the modeling of a BZ reaction [14,[22][23][24][25][26][27][28][29][30][31][32][33].…”

Section: Short Overview Of the Belousov − Zhabotinsky Reactionmentioning

confidence: 99%

Current rates and reaction rates in the Stoichiometric Network Analysis (SNA)

et al. 2014

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Abstract:In stoichiometric network analysis (SNA) the instability condition is calculated by the current rates. Recently, we have shown that in the final result the current rates can be substituted by reaction rates, which is a more appropriate value for the examination of instability from experimental point of view. Here, we elaborate the problem of whether the current rates are necessary parameters in the calculation, with the aim of obtaining the region of instability. All calculations are performed on a model for Belousov-Zhabotinsky (BZ) reaction, which has not been examined by SNA.

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Modelling complex transient oscillations for the BZ reaction in a batch reactor

Cited by 33 publications

References 11 publications

Numerical Analysis of Transient and Periodic Dynamics in Single and Coupled Nagumo–sato Models

Numerical Analysis of Transient and Periodic Dynamics in Single and Coupled Nagumo–sato Models

Lyapunov exponents and the Belousov-Zhabotinsky oscillator: an interactive computational approach

Current rates and reaction rates in the Stoichiometric Network Analysis (SNA)

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