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Article Dans Une Revue Journal of Mathematical Biology Année : 2023

From the distributions of times of interactions to preys and predators dynamical systems

Résumé

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.
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Dates et versions

hal-03183538 , version 1 (29-03-2021)
hal-03183538 , version 2 (18-05-2021)

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Vincent Bansaye, Bertrand Cloez. From the distributions of times of interactions to preys and predators dynamical systems. Journal of Mathematical Biology, 2023, 87 (2), ⟨10.1007/s00285-023-01925-5⟩. ⟨hal-03183538v2⟩
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