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Exact Reduction of the Generalized Lotka–Volterra Equations via Integral and Algebraic Substitutions

Department of Computer Science, University of Colorado Boulder, Boulder, CO 80309-0430, USA
Academic Editors: Rainer Breitling and Karlheinz Schwarz
Computation 2021, 9(5), 49; https://doi.org/10.3390/computation9050049
Received: 27 February 2021 / Revised: 13 April 2021 / Accepted: 19 April 2021 / Published: 22 April 2021
(This article belongs to the Section Computational Biology)
Systems of interacting species, such as biological environments or chemical reactions, are often described mathematically by sets of coupled ordinary differential equations. While a large number β of species may be involved in the coupled dynamics, often only α<β species are of interest or of consequence. In this paper, we explored how to construct models that include only those given α species, but still recreate the dynamics of the original β-species model. Under some conditions detailed here, this reduction can be completed exactly, such that the information in the reduced model is exactly the same as the original one, but over fewer equations. Moreover, this reduction process suggests a promising type of approximate model—no longer exact, but computationally quite simple. View Full-Text
Keywords: generalized Lotka–Volterra equations; exact reduction; algebraic substitutions; memory kernel generalized Lotka–Volterra equations; exact reduction; algebraic substitutions; memory kernel
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MDPI and ACS Style

Morrison, R.E. Exact Reduction of the Generalized Lotka–Volterra Equations via Integral and Algebraic Substitutions. Computation 2021, 9, 49. https://doi.org/10.3390/computation9050049

AMA Style

Morrison RE. Exact Reduction of the Generalized Lotka–Volterra Equations via Integral and Algebraic Substitutions. Computation. 2021; 9(5):49. https://doi.org/10.3390/computation9050049

Chicago/Turabian Style

Morrison, Rebecca E. 2021. "Exact Reduction of the Generalized Lotka–Volterra Equations via Integral and Algebraic Substitutions" Computation 9, no. 5: 49. https://doi.org/10.3390/computation9050049

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