Mathematical Modeling of Cyclic Population Dynamics

Speaker
Alexander Nepomnyashchy
Date
12/12/2019 - 15:00 - 14:00Add to Calendar 2019-12-12 14:00:00 2019-12-12 15:00:00 Mathematical Modeling of Cyclic Population Dynamics :abstract   We consider deterministic models for three-species ecological systems exhibiting cyclic (rock-paper-scissors) dynamics, which account for delay or/and spatial nonlocality in interspecies competition. The biological origin of the temporal and spatial nonlocalities is the secretion of a toxin lethal to another species in the environment. The dynamics of spatially homogeneous states is described by ODE models, which allow for three classes of stable limit solution: (i) steady coexistence solutions; (ii) limit cycles; (iii) stable heteroclinic cycles. PDE models allow to describe the nontrivial spatial structure and dynamics of fronts between domains occupied by homogeneous states, as well as regular and irregular spatio-temporal dynamical regimes. Generalizations for multispecies systems are discussed. Bldg. 216, Room 201 אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Bldg. 216, Room 201
Abstract

:abstract
 

We consider deterministic models for three-species ecological systems
exhibiting cyclic (rock-paper-scissors) dynamics, which account for delay
or/and spatial nonlocality in interspecies competition. The biological
origin of the temporal and spatial nonlocalities is the secretion of a
toxin lethal to another species in the environment. The dynamics of
spatially homogeneous states is described by ODE models, which allow for
three classes of stable limit solution: (i) steady coexistence solutions;
(ii) limit cycles; (iii) stable heteroclinic cycles. PDE models allow to
describe the nontrivial spatial structure and dynamics of fronts between
domains occupied by homogeneous states, as well as regular and irregular
spatio-temporal dynamical regimes. Generalizations for multispecies
systems are discussed.

Last Updated Date : 10/12/2019