NASSOR, Mme Hiba (2024) Étude théorique et exploration numérique et statistique autour du paradoxe stability-diversity PRE - Research Project, ENSTA.
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Abstract
This work explores numerically and statistically some aspects of the dynamics of interactions between different strains within host populations and their stability, based on the replicator equation. Inspired by the stability-diversity debate, and using the concepts developed by Sten Madec and Erida Gjini (2021), in particular on the probability of stable coexistence of k strains in a pool of N strains, our study focuses on steady states, saturated steady states and stable steady states, their average number as well as the distribution of steady, saturated and stable states with exactly k strains, in configurations where all interactions are considered random and independent, and subsequently by introducing the ratio of single to co-colonization $\mu$. Our approach includes numerical simulations and probabilistic calculations in order to identify indicators to qualify steady, saturated and stable states and to study those with exactly k strains. We also study the impact of the $\mu$ parameter on these dynamics. The results reveal varied behaviors and show that this ratio strongly influences the dynamic complexity of the system.
Item Type: | Thesis (PRE - Research Project) |
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Uncontrolled Keywords: | Replicator equation - Coexistence - Stable steady state - Saturated steady state - co-colonization - Monte-Carlo |
Subjects: | Mathematics and Applications |
ID Code: | 10061 |
Deposited By: | Hiba NASSOR |
Deposited On: | 02 sept. 2024 15:06 |
Dernière modification: | 11 sept. 2024 13:06 |
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