title: Memory and adaptive behavior in population dynamics: anti-predator behavior as a case study.
abstract: Memory allows organisms to forecast the future on the basis of experience, and thus, in some form, is important for the development of flexible adaptive behavior by animal communities. To model memory, we use the concept of hysteresis, which mathematically is described by the Preisach operator. As a case study, we consider anti-predator adaptation in the classic Lotka-Volterra predator-prey model. Despite its simplicity, the model allows us 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. The main factor that determines the actual equilibrium state to which a trajectory converges is the maximal number achieved by the population of predator along this trajectory.
authors.affiliation: Weierstrass Institute, Berlin, Germany.
authors.forename: Alexander
authors.initials: A
authors.lastname: Pimenov
authors.affiliation: University College Cork, Cork, Ireland.
authors.forename: Thomas C
authors.initials: TC
authors.lastname: Kelly
authors.affiliation: Centre de Recerca Matemática, Barcelona, Spain.
authors.forename: Andrei
authors.initials: A
authors.lastname: Korobeinikov
authors.affiliation: University College Cork, Cork, Ireland.
authors.forename: Michael J
authors.initials: MJ
authors.lastname: O'Callaghan
authors.affiliation: The University of Texas at Dallas, Richardson, USA. dmitry.rachinskiy@utdallas.edu.
authors.forename: Dmitrii
authors.identifier: 0000-0003-2786-7205
authors.initials: D
authors.lastname: Rachinskii
mesh_terms: D000222:Adaptation, Physiological; D000223:Adaptation, Psychological; D000818:Animals; D003198:Computer Simulation; D017753:Ecosystem; D020387:Food Chain; D055641:Mathematical Concepts; D008568:Memory / Q000502:physiology*; D008954:Models, Biological; D008960:Models, Psychological; D011157:Population Dynamics; D011235:Predatory Behavior / Q000502:physiology*
keywords: Adaptation; Bi-stability; Hysteresis; Predator-prey model; Preisach operator; Refuge