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.