2021/03/30 by Vincent Bansaye, Bansaye, Vincent, Bertand Cloez +1
Mathematics · Medicine · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · doi:10.48550/arxiv.2103.16303
openalex publication_date 2021/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a stochastic individual based model where each predator searches during a random time and then manipulates its prey or rests. The time distributions may be non-exponential. An age structure allows to describe these interactions and get a Markovian setting. The process is characterized by a measure-valued stochastic differential equation. We prove averaging results in this infinite dimensional setting and get the convergence of the slow-fast macroscopic prey predator process to a two dimensional dynamical system. We recover classical functional responses. We also get new forms arising in particular when births and deaths of predators are affected by the lack of food.