Bursting in the Belousov-Zhabotinsky Reaction Added with Phenol in a Batch Reactor

Cadena, Ariel; Ágreda, Jesús

doi:10.5935/0103-5053.20130254

Cited by 3 publications

(2 citation statements)

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“…(Hilborn, 2004) In here considered case, intermittent dynamic state (also known as intermittent oscillations, intermittent chaos, or simply intermittency) (Pomeau and Manneville, 1980;Hilborn, 2004;Schuster and Just, 2005) represents a chaotic mixture of large amplitude relaxation oscillations grouped in bursts, and between them, there are small-amplitude sinusoidal oscillations or quiescent parts, known as gaps. This type of deterministic dynamic phenomenon may also be found in some complex chemical (Chopin-Dumas, 1978;Pomeau et al, 1981;Roux et al, 1981;Baier et al, 1989;Kreisberg et al, 1991;Strizhak and Menzinger, 1996;Vukojević et al, 2000;Kolar-Anić et al, 2004;Cadena et al, 2013;Čupić et al, 2014;Bubanja et al, 2016Bubanja et al, , 2017 and biochemical (Izhikevich, 2000a,b) reaction systems under conditions that do not have an equilibrium.…”

Section: Introductionmentioning

confidence: 84%

Intermittent Chaos in the CSTR Bray–Liebhafsky Oscillator-Specific Flow Rate Dependence

et al. 2020

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Dynamic states with intermittent oscillations consist of a chaotic mixture of large amplitude relaxation oscillations grouped in bursts, and between them, small-amplitude sinusoidal oscillations, or even the quiescent parts, known as gaps. In this study, intermittent dynamic states were generated in Bray-Liebhafsky (BL) oscillatory reaction in an isothermal continuously-fed, well-stirred tank reactor (CSTR) controled by changes of specific flow rate. The intermittent states were found between two regular periodic states and obtained for specific flow rate values from 0.020 to 0.082 min −1. Phenomenological analysis based on the quantitative characteristics of intermittent oscillations, as well as, the largest Lyapunov exponents calculated from experimentally obtained time series, both indicated the same type of behavior. Namely, fully developed chaos arises when approaching to the vertical asymptote which is somewhere between two bifurcations. Hence, this study proposes described route to fully developed chaos in the Bray-Liebhafsky oscillatory reaction as an explanation for experimentally observed intermittent dynamics. This is in correlation with our previously obtained results where the most chaotic intermittent chaos was achieved between the periodic oscillatory dynamic state and stable steady state, generated in BL under CSTR conditions by varying temperature and inflow potassium iodate concentration. Moreover, it was shown that, besides the largest Lyapunov exponent, analysis of chaos in experimentally obtained intermittent states can be achieved by a simpler approach which involves using the quantitative characteristics of the BL reaction evolution, that is, the number and length of gaps and bursts obtained for the various values of specific flow rates.

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Section: Introductionmentioning

confidence: 84%

Intermittent Chaos in the CSTR Bray–Liebhafsky Oscillator-Specific Flow Rate Dependence

et al. 2020

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“…However, when the two frequencies are both much less than 1 and the fast-slow dynamical characteristics still remain in the system, a phenomenon known as bursting may arise [5,6]. This phenomenon can occur in dynamical systems whose variables evolve on two different time scales, and it has potential applications in physics [9,10], mechanics [11], biology [12,13], chemistry [14,15], neuroscience [5,6], information encoding and computation [16], and in engineering systems [17,18]. The potential use of bursting in order to achieve extremely rapid actuators was recently demonstrated [19] in electromechanical systems .…”

Section: Introductionmentioning

confidence: 99%

Novel bursting oscillations in a nonlinear gyroscope oscillator

et al. 2022

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We report the occurrence of bursting oscillations in a gyroscope oscillator driven by low-frequency external period forcing. The bursting patterns arise when either the frequency or amplitude of the excitation force is varied. They take the form of pulse-shaped explosions (PSEs) wherein periodic attractors of lower periodicity disappear due to the loss of asymptotic stability of the equilibrium point between resting and active states. The process involves the appearance of zero eigenvalues and the creation of new attractors of higher periodicity. Both point-cycle and cycle-cycle bursting is seen. It is accompanied by the birth of periodic attractors, ranging from period one to period four, depending on an integer n in the frequency of the parametric driving force. The dynamics of the oscillator is shown to exhibit a fold bifurcation related to critical escape transitions.

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Inverse period-doubling bifurcations determine complex structure of bursting in a one-dimensional non-autonomous map

Han

Chen

2016

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We propose a simple one-dimensional non-autonomous map, in which some novel bursting patterns (e.g., "fold/double inverse flip" bursting, "fold/multiple inverse flip" bursting, and "fold/a cascade of inverse flip" bursting) can be observed. Typically, these bursting patterns exhibit complex structures containing a chain of inverse period-doubling bifurcations. The active states related to these bursting can be period-2(n) (n = 1, 2, 3,…) attractors or chaotic attractors, which may evolve to quiescence by a chain of inverse period-doubling bifurcations when the slow excitation decreases through period-doubling bifurcation points of the map. This accounts for the complex inverse period-doubling bifurcation structures observed in bursting patterns. Our findings enrich the possible routes to bursting as well as the underlying mechanisms of bursting.

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Bursting in the Belousov-Zhabotinsky Reaction Added with Phenol in a Batch Reactor

Cited by 3 publications

References 1 publication

Intermittent Chaos in the CSTR Bray–Liebhafsky Oscillator-Specific Flow Rate Dependence

Intermittent Chaos in the CSTR Bray–Liebhafsky Oscillator-Specific Flow Rate Dependence

Novel bursting oscillations in a nonlinear gyroscope oscillator

Inverse period-doubling bifurcations determine complex structure of bursting in a one-dimensional non-autonomous map

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