Coarse-graining the cyclic lotka-volterra model: SSA and local maximum likelihood estimation

C. P. Calderon, G. A. Tsekouras, A. Provata, I. G. Kevrekidis

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Scopus citations

Abstract

When the output of an atomistic simulation (such as the Gillespie stochastic simulation algorithm, SSA) can be approximated as a diffusion process, we may be interested in the dynamic features of the deterministic (drift) component of this diffusion. We perform traditional scientific computing tasks (integration, steady state and closed orbit computation, and stability analysis) on such a drift component using a SSA simulation of the Cyclic Lotka-Volterra system as our illustrative example. The results of short bursts of appropriately initialized SSA simulations are used to fit local diffusion models using Aït-Sahalia's transition density expansions [1], [2], [3] in a maximum likelihood framework. These estimates are then coupled with standard numerical algorithms (such as Newton-Raphson or numerical integration routines) to help design subsequent SSA experiments. A brief discussion of the validity of the local diffusion approximation of the SSA simulation (a jump process) is included.

Original languageEnglish (US)
Title of host publicationModel Reduction and Coarse-Graining Approaches for Multiscale Phenomena
PublisherSpringer Berlin Heidelberg
Pages247-267
Number of pages21
ISBN (Print)3540358854, 9783540358855
DOIs
StatePublished - Dec 1 2006

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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    Calderon, C. P., Tsekouras, G. A., Provata, A., & Kevrekidis, I. G. (2006). Coarse-graining the cyclic lotka-volterra model: SSA and local maximum likelihood estimation. In Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena (pp. 247-267). Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-35888-9_11