Accarino, Chiara (2025) Unveiling stability: a mathematical journey from theory to biological systems. [Tesi di dottorato]
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| Tipologia del documento: | Tesi di dottorato |
|---|---|
| Lingua: | English |
| Titolo: | Unveiling stability: a mathematical journey from theory to biological systems |
| Autori: | Autore Email Accarino, Chiara chiara.accarino@unina.it |
| Data: | 8 Febbraio 2025 |
| Numero di pagine: | 150 |
| Istituzione: | Università degli Studi di Napoli Federico II |
| Dipartimento: | Matematica e Applicazioni "Renato Caccioppoli" |
| Dottorato: | Matematica e Applicazioni |
| Ciclo di dottorato: | 37 |
| Coordinatore del Corso di dottorato: | nome email Moscariello, Gioconda gioconda.moscariello@unina.it |
| Tutor: | nome email Capone, Florinda [non definito] |
| Data: | 8 Febbraio 2025 |
| Numero di pagine: | 150 |
| Parole chiave: | Linear stability, patterns, biofilm |
| Settori scientifico-disciplinari del MIUR: | Area 01 - Scienze matematiche e informatiche > MAT/07 - Fisica matematica |
| Informazioni aggiuntive: | Faccio parte del 37° ciclo di dottorato. |
| Depositato il: | 29 Ott 2025 09:18 |
| Ultima modifica: | 12 Ago 2026 05:38 |
| URI: | https://www.fedoa.unina.it/id/eprint/16662 |
Abstract
This doctoral thesis investigates the stability of stationary solutions in dynamical systems, applying Lyapunov's stability theory to various mathematical models with relevance to biology and ecology. It is organized into three main sections: a comprehensive technical background, an overview of recent advancements in reaction-diffusion models, and an exploration of their applications in various biological and ecological contexts. The research is based on both linear and nonlinear stability theory, complemented by numerical simulations, to enhance the understanding of spatial and temporal dynamics in a variety of physical and biological systems. The study is structured around three mathematical models: 1) a Leslie-Gower predator-prey model with intraguild predation, analyzing species interactions and coexistence; 2) a biofilm growth model with inhibition, examining the effects of nonlinear kinetics and spatial interactions on stability; 3) a reaction-diffusion model for Mycobacterium tuberculosis infection, incorporating weakly nonlinear analysis to explore pattern formation and chemotaxis-driven instability. The thesis combines theoretical analysis with numerical simulations to provide insights into the interplay between diffusion, reaction kinetics, and stability. By bridging mathematical theory with applications in ecology and epidemiology, this work contributes to the broader understanding of stability in complex biological systems.
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