Numerical simulation of stochastic replicator models in catalyzed RNA-like polymers

Andreas Rößler, Mohammed Seaïd and Mostafa Zahri

Mathematics and Computers in Simulation (MATCOM), 2009, vol. 79, issue 12, 3577-3586

Abstract: A stochastic model for replicators in catalyzed RNA-like polymers is presented and numerically solved. The model consists of a system of reaction–diffusion equations describing the evolution of a population formed by RNA-like molecules with catalytic capabilities in a prebiotic process. The diffusion effects and the catalytic reactions are deterministic. A stochastic excitation with additive noise is introduced as a force term. To numerically solve the governing equations we apply the stochastic method of lines. A finite-difference reaction–diffusion system is constructed by discretizing the space and the associated stochastic differential system is numerically solved using a class of stochastic Runge–Kutta methods. Numerical experiments are carried out on a prototype of four catalyzed selfreplicator species along with an activated and an inactivated residues. Results are given in two space dimensions.

Keywords: Stochastic replicator models; Reaction–diffusion equations; Method of lines; Additive noise; Stochastic Runge–Kutta schemes (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:79:y:2009:i:12:p:3577-3586

DOI: 10.1016/j.matcom.2009.04.018

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