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Growth Quakes and Stasis Using Iterations of Inflating Complex Random Matrices

I extend to the case of complex matrices, rather than the case of real matrices as in a prior study, a method of iterating the operation of an “inflating random matrix” onto a state vector to describe complex growing systems. I show that the process also describes in this complex case a punctuated g...

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Autor principal: Benisty, Henri
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10670579/
https://www.ncbi.nlm.nih.gov/pubmed/37998199
http://dx.doi.org/10.3390/e25111507
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author Benisty, Henri
author_facet Benisty, Henri
author_sort Benisty, Henri
collection PubMed
description I extend to the case of complex matrices, rather than the case of real matrices as in a prior study, a method of iterating the operation of an “inflating random matrix” onto a state vector to describe complex growing systems. I show that the process also describes in this complex case a punctuated growth with quakes and stasis. I assess that under one such inflation step, the vector will shift to a really different one (quakes) only if the inflated matrix has sufficiently dominant new eigenvectors. The vector shall prefer stasis (a similar vector) otherwise, similar to the real-valued matrices discussed in a prior study. Specifically, in order to extend the model relevance, I assess that under various update schemes of the system’s representative vector, the bimodal distribution of the changes of the dominant eigenvalue remains the core concept. Overall, I contend that the punctuations may appropriately address the issue of growth in systems combining a large weight of history and some sudden quake occurrences, such as economic systems or ecological systems, with the advantage that unpaired complex eigenvalues provide more degrees of freedom to suit real systems. Furthermore, random matrices could be the right meeting point for exerting thermodynamic analogies in a reasonably agnostic manner in such rich contexts, taking into account the profusion of items (individuals, species, goods, etc.) and their networked, tangled interactions 50+ years after their seminal use in R.M. May’s famous “interaction induced instability” paradigm. Finally, I suggest that non-ergodic tools could be further applied for tracking the specifics of large-scale evolution paths and for checking the model’s relevance to the domains mentioned above.
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spelling pubmed-106705792023-10-31 Growth Quakes and Stasis Using Iterations of Inflating Complex Random Matrices Benisty, Henri Entropy (Basel) Article I extend to the case of complex matrices, rather than the case of real matrices as in a prior study, a method of iterating the operation of an “inflating random matrix” onto a state vector to describe complex growing systems. I show that the process also describes in this complex case a punctuated growth with quakes and stasis. I assess that under one such inflation step, the vector will shift to a really different one (quakes) only if the inflated matrix has sufficiently dominant new eigenvectors. The vector shall prefer stasis (a similar vector) otherwise, similar to the real-valued matrices discussed in a prior study. Specifically, in order to extend the model relevance, I assess that under various update schemes of the system’s representative vector, the bimodal distribution of the changes of the dominant eigenvalue remains the core concept. Overall, I contend that the punctuations may appropriately address the issue of growth in systems combining a large weight of history and some sudden quake occurrences, such as economic systems or ecological systems, with the advantage that unpaired complex eigenvalues provide more degrees of freedom to suit real systems. Furthermore, random matrices could be the right meeting point for exerting thermodynamic analogies in a reasonably agnostic manner in such rich contexts, taking into account the profusion of items (individuals, species, goods, etc.) and their networked, tangled interactions 50+ years after their seminal use in R.M. May’s famous “interaction induced instability” paradigm. Finally, I suggest that non-ergodic tools could be further applied for tracking the specifics of large-scale evolution paths and for checking the model’s relevance to the domains mentioned above. MDPI 2023-10-31 /pmc/articles/PMC10670579/ /pubmed/37998199 http://dx.doi.org/10.3390/e25111507 Text en © 2023 by the author. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Benisty, Henri
Growth Quakes and Stasis Using Iterations of Inflating Complex Random Matrices
title Growth Quakes and Stasis Using Iterations of Inflating Complex Random Matrices
title_full Growth Quakes and Stasis Using Iterations of Inflating Complex Random Matrices
title_fullStr Growth Quakes and Stasis Using Iterations of Inflating Complex Random Matrices
title_full_unstemmed Growth Quakes and Stasis Using Iterations of Inflating Complex Random Matrices
title_short Growth Quakes and Stasis Using Iterations of Inflating Complex Random Matrices
title_sort growth quakes and stasis using iterations of inflating complex random matrices
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10670579/
https://www.ncbi.nlm.nih.gov/pubmed/37998199
http://dx.doi.org/10.3390/e25111507
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