Chemical reaction systems with a low to moderate number of molecules are typically modeled as discrete jump Markov processes. These systems are oftentimes simulated with methods that produce statistically exact sample paths such as the Gillespie algorithm or the next reaction method. In this paper we make explicit use of the fact that the initiation times of the reactions can be represented as the firing times of independent, unit rate Poisson processes with internal times given by integrated propensity functions. Using this representation we derive a modified next reaction method and, in a way that achieves efficiency over existing approaches for exact simulation, extend it to systems with time dependent propensities as well as to systems with delays.
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7 December 2007
Research Article|
December 06 2007
A modified next reaction method for simulating chemical systems with time dependent propensities and delays
David F. Anderson
David F. Anderson
a)
Department of Mathematics,
University of Wisconsin-Madison
, Madison, Wisconsin 53706, USA
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Electronic mail: [email protected]. URL: www.math.wisc.edu∕∼anderson
J. Chem. Phys. 127, 214107 (2007)
Article history
Received:
June 20 2007
Accepted:
September 26 2007
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Citation
David F. Anderson; A modified next reaction method for simulating chemical systems with time dependent propensities and delays. J. Chem. Phys. 7 December 2007; 127 (21): 214107. https://doi.org/10.1063/1.2799998
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