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

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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https://hal.archives-ouvertes.fr/hal-03183538
Contributor : Vincent Bansaye <>
Submitted on : Monday, March 29, 2021 - 6:49:20 PM
Last modification on : Wednesday, March 31, 2021 - 3:04:49 PM

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  • HAL Id : hal-03183538, version 1
  • ARXIV : 2103.16303

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Vincent Bansaye, Bertrand Cloez. From the distributions of times of interactions to preys and predators dynamical systems. 2021. ⟨hal-03183538⟩

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