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arXiv · 2103.16303

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

Vincent Bansaye·Bertand Cloez
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Abstract

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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Vincent Bansaye, Bertand Cloez. 2021-03-30. From the distributions of times of interactions to preys and predators dynamical systems. https://arxiv.org/abs/2103.16303

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