Deterministic chaos in serially coupled chemical oscillators

Doumbouya, Sory I.; Muenster, A.; Doona, Christopher J.; Schneider, F. W.

doi:10.1021/j100107a009

Cited by 28 publications

(16 citation statements)

References 5 publications

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“…The substrate (N-benzoyl-L-arginine ethyl ester) is also positively charged in a broad range of pH (we assume z s = +1) and plays a role of an inhibitor (negative feedback species [27]). (12), (13). In addition, the rapidly equilibrating dissociation of water ties H + and OH − together via a constant product of their concentrations as assumed in deriving Eqs.…”

Section: Discussionmentioning

confidence: 99%

“…The dynamical equations (12), (13) together with (16) constitute a system of periodically forced nonautonomous ODEs [26]. maximal negative or positive field) and T is the period of the forcing.…”

Section: Effects Of Alternating Electric Fieldmentioning

confidence: 99%

“…This is especially valid in microfluidics and in microchips, particularly for reactions as PCR (polymerase chain reaction) and separations via electrophoresis, see, for example [1]. The diffusion-like coupling by itself may cause many interesting dynamical phenomena [5][6][7][8][9][10][11][12][13][14][15][16]. The problem of continuous distribution of the concentrations in the reactor can be simplified to a coupled cell system if the system is compartmentalized and stirred vigorously in each compartment.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Electric Field Effects on an Enzyme Membrane Oscillator

Schreiber¹,

Hasal²,

Marek³

2002

Zeitschrift Für Physikalische Chemie

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A simple two compartment model system composed of a reservoir and a reactor is studied by means of numerical bifurcation analysis. An enzyme reaction involving ionic species is assumed to take place in the reactor connected to the reservoir via a semi-permeable electrically inert membrane. An external electric voltage is applied to this system via electrodes connected to each of the two compartments. An intra-membrane electric field caused by the applied voltage generates electrophoretic fluxes of each charged reaction component. We study the effects of a static and a periodically varying electric field on the dynamical regimes in the reactor. In the static case we find that a negative field supports the oscillatory dynamics while a positive field promotes multiplicity. Sinusoidal variations of the field cause a rich variety of dynamical responses, ranging from various periodic firing patterns to quasiperiodicity and chaos. These dynamical modes are associated with characteristic bifurcation structures in a forcing period -forcing amplitude bifurcation diagram which can be used for their classification.

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Section: Discussionmentioning

confidence: 99%

Section: Effects Of Alternating Electric Fieldmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Electric Field Effects on an Enzyme Membrane Oscillator

Schreiber¹,

Hasal²,

Marek³

2002

Zeitschrift Für Physikalische Chemie

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“…Consequently, examples of chaotic dynamics were reported in chemistry as motion associated with simple chemical reactions [5]- [7]. Another example is deterministic chaos coming as the result of coupling chemical oscillators [8], [9]. Papers mentioned above are focused on analysis of the mathematical models that eventually turns to be aperiodic and/or chaotic.…”

Section: Introductionmentioning

confidence: 99%

Minimal Realizations of Autonomous Chaotic Oscillators Based on Trans-Immittance Filters

Petržela

Polák

2019

IEEE Access

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This review paper describes a design process toward fully analog realizations of chaotic dynamics that can be considered canonical (minimum number of the circuit elements), robust (exhibit structurally stable strange attractors), and novel. Each autonomous chaotic lumped circuit proposed in this paper can be understood as a looped system, where linear trans-immittance frequency filter interacts with an active nonlinear two-port. The existence of chaos is demonstrated via well-established numerical algorithms that represent the current standard in the field of nonlinear dynamics, i.e., by calculation of the largest Lyapunov exponent and high-resolution 1-D bifurcation diagrams. The achieved numerical results are put into the context of experimental measurement; observed state trajectories prove a one-to-one correspondence between theoretical expectations and practical outputs, i.e., prescribed strange attractors do not represent the chaotic transients. Finally, short term unpredictability of the chaotic flow is demonstrated via calculation of Kaplan-Yorke dimension that is high, i.e., generated waveforms can find interesting applications in the fields of chaotic masking, modulation, or chaos-based cryptography.

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“…Experiments have been carried out using batch reactors, as well as CSTR reactors. [1][2][3][4][5][6][7][8] The simplest system in which the coupling can be studied is a single solution. The coupling that occurs inside the same solution is very interesting; as in a closed reactor, the different parts of the solution are obviously physically coupled.…”

Section: Introductionmentioning

confidence: 99%