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

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  • Rößler, Andreas
  • Seaïd, Mohammed
  • Zahri, Mostafa

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.

Suggested Citation

  • Rößler, Andreas & Seaïd, Mohammed & Zahri, Mostafa, 2009. "Numerical simulation of stochastic replicator models in catalyzed RNA-like polymers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(12), pages 3577-3586.
    • Handle: RePEc:eee:matcom:v:79:y:2009:i:12:p:3577-3586
    DOI: 10.1016/j.matcom.2009.04.018
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    References listed on IDEAS

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    1. Kwiecinska, Anna A., 1999. "Stabilization of partial differential equations by noise," Stochastic Processes and their Applications, Elsevier, vol. 79(2), pages 179-184, February.
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