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Title: Memory and adaptive behaviour in population dynamics: Anti-predator behaviour as a case study
Authors: Pimenov, AlexanderKelly, Thomas C.Korobeinikov, AndreiOCallaghan, Michael J.Rachinskii, Dmitrii
Issue Date: 2015
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 2157, ISSN 2198-5855
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: Memory enables to forecast future on the basis of experience, and thus, in some form, is principally important for the development of flexible adaptive behaviour by animal communities. To model memory, in this paper we use the concept of hysteresis, which mathematically is described by the Preisach operator. As case study, we consider anti-predator adaptation in the classic Lotka-Volterra predator-prey model. Despite its simplicity, the model allows to naturally incorporate essential features of an adaptive system and memory. Our analysis and simulations show that a system with memory can have a continuum of equilibrium states with non-trivial stability properties.
Keywords: Bi-stability; Preisach operator; hysteresis; adaptation; predator-prey model; refuge
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
Appears in Collections:Mathematik

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