Numerical Simulation of Stochastic Replicator Models in Catalyzed RNA-like Polymers.

Rößler, A.; Seaid, M.; Zahri, M.

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.

Citation

Rößler, A., Seaid, M., & Zahri, M. (2009). Numerical Simulation of Stochastic Replicator Models in Catalyzed RNA-like Polymers. Mathematics and Computers in Simulation, 79(12), 3577-3586. https://doi.org/10.1016/j.matcom.2009.04.018

• Journal Article Type: Article
• Publication Date: 2009-08
• Journal: Mathematics and Computers in Simulation
• Print ISSN: 0378-4754
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 79
• Issue: 12
• Pages: 3577-3586
• DOI: https://doi.org/10.1016/j.matcom.2009.04.018
• Keywords: Stochastic replicator models, Reaction–diffusion equations, Method of lines, Additive noise, Stochastic Runge–Kutta schemes.