Stochastic Analysis of an Oscillating Chemical Reaction

Nakanishi, Tetsuo

doi:10.1143/jpsj.32.1313

Cited by 8 publications

(2 citation statements)

References 7 publications

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“…The version of the SSA described above is the one originally presented in References 8 and 9. A number of earlier works applied similar if not equivalent procedures to specific model systems (13)(14)(15)(16)(17)(18)(19) but paid little attention to developing the supporting theory. In this section I focus on some later elaborations on and improvements to the SSA.…”

Section: Elaborations On and Improvements To The Stochastic Simulatiomentioning

confidence: 99%

Stochastic Simulation of Chemical Kinetics

Gillespie

2007

Annu. Rev. Phys. Chem.

1,846

1,819

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Stochastic chemical kinetics describes the time evolution of a well-stirred chemically reacting system in a way that takes into account the fact that molecules come in whole numbers and exhibit some degree of randomness in their dynamical behavior. Researchers are increasingly using this approach to chemical kinetics in the analysis of cellular systems in biology, where the small molecular populations of only a few reactant species can lead to deviations from the predictions of the deterministic differential equations of classical chemical kinetics. After reviewing the supporting theory of stochastic chemical kinetics, I discuss some recent advances in methods for using that theory to make numerical simulations. These include improvements to the exact stochastic simulation algorithm (SSA) and the approximate explicit tau-leaping procedure, as well as the development of two approximate strategies for simulating systems that are dynamically stiff: implicit tau-leaping and the slow-scale SSA.

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Section: Elaborations On and Improvements To The Stochastic Simulatiomentioning

confidence: 99%

Stochastic Simulation of Chemical Kinetics

Gillespie

2007

Annu. Rev. Phys. Chem.

1,846

1,819

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show abstract

“…Averaging over sufficiently many such realizations can yield estimates of any average that is computable from the solution P(x, t | x 0 , t 0 ) of the CME, and examining only a few realizations often yields insights that are not obvious from P(x, t | x 0 , t 0 ). The earliest known constructions of simulated trajectories were made in 1972 by Nakanishi 14 and Šolc and Horsák, 15 and in 1974 by…”

Section: The Stochastic Simulation Algorithmmentioning

confidence: 99%

Perspective: Stochastic algorithms for chemical kinetics

Gillespie

Hellander²,

Petzold³

2013

The Journal of Chemical Physics

300

341

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We outline our perspective on stochastic chemical kinetics, paying particular attention to numerical simulation algorithms. We first focus on dilute, well-mixed systems, whose description using ordinary differential equations has served as the basis for traditional chemical kinetics for the past 150 years. For such systems, we review the physical and mathematical rationale for a discretestochastic approach, and for the approximations that need to be made in order to regain the traditional continuous-deterministic description. We next take note of some of the more promising strategies for dealing stochastically with stiff systems, rare events, and sensitivity analysis. Finally, we review some recent efforts to adapt and extend the discrete-stochastic approach to systems that are not wellmixed. In that currently developing area, we focus mainly on the strategy of subdividing the system into well-mixed subvolumes, and then simulating diffusional transfers of reactant molecules between adjacent subvolumes together with chemical reactions inside the subvolumes. © 2013 AIP Publishing LLC.[http://dx

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Photoinitiated bulk polymerization of furfuryl methacrylate. Stochastic simulation results using the new model CORUB

Davidenko

Alvarez

2001

Computational and Theoretical Polymer Science

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Stochastic Analysis of an Oscillating Chemical Reaction

Cited by 8 publications

References 7 publications

Stochastic Simulation of Chemical Kinetics

Stochastic Simulation of Chemical Kinetics

Perspective: Stochastic algorithms for chemical kinetics

Photoinitiated bulk polymerization of furfuryl methacrylate. Stochastic simulation results using the new model CORUB

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