Probability Analysis of Selected Population Models - SETTATI, Adel;LAHROUZ, Aadil;EL IDRISSI, Mourad
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This book explores the dynamics of some population models under stochastic perturbations and regime switching across different environmental patches. By integrating Markovian switching processes, we investigate the stability and ergodicity characteristics of the model, providing insights into how random fluctuations and discrete regime shifts impact population persistence and extinction probabilities. The research initially focuses on the stability and ergodicity of some stochastic models under regime switching, highlighting how environmental variability across patches influences the long-term…mehr

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Produktbeschreibung
This book explores the dynamics of some population models under stochastic perturbations and regime switching across different environmental patches. By integrating Markovian switching processes, we investigate the stability and ergodicity characteristics of the model, providing insights into how random fluctuations and discrete regime shifts impact population persistence and extinction probabilities. The research initially focuses on the stability and ergodicity of some stochastic models under regime switching, highlighting how environmental variability across patches influences the long-term behavior of the population. Mathematical analysis and numerical simulations demonstrate that the model exhibits varying degrees of stability depending on the stochastic parameters and the switching mechanisms involved. Further, the analysis extends to the impact of Markovian switching on the population model, elucidating how changes in environmental states governed by a Markov process affect population dynamics. This study examines the conditions under which the population persists or faces extinction, considering both slow and fast switching regimes.
Autorenporträt
Adel Settati is an esteemed full Professor of Mathematics at the Faculty of Sciences and Technology (FSTT) in Tangier, Morocco. He completed his doctoral studies in probability at the renowned University of Rennes 1 in France. His primary research interests revolve around dynamic systems, applied probability, and stochastic epidemics.