Canard doublet in a Lotka-Volterra type model

Extinction in Lotka-Volterra model

Competitive birth-death processes often exhibit an oscillatory behavior. We investigate a particular case where the oscillation cycles are marginally stable on the mean-field level. An iconic example of such a system is the Lotka-Volterra model of predator-prey competition. Fluctuation effects due to discreteness of the populations destroy the mean-field stability and eventually drive the syste...

Fixation in a cyclic Lotka-Volterra model

We study a cyclic Lotka-Volterra model of N interacting species populating a d-dimensional lattice. In the realm of a Kirkwood approximation, a critical number of species Nc(d) above which the system fixates is determined analytically. We find Nc = 5, 14, 23 in dimensions d = 1, 2, 3, in remarkably good agreement with simulation results in two dimensions. A cyclic variant of the Lotka-Volterra ...

Stochastic delay Lotka–Volterra model

We reveal in this paper that the environmental noise will not only suppress a potential population explosion in the stochastic delay Lotka–Volterra model but will also make the solutions to be stochastically ultimately bounded. To reveal these interesting facts, we stochastically perturb the delay Lotka–Volterra model ẋ(t) = diag(x1(t), . . . , xn(t))[b + Ax(t − τ)] into the Itô form dx(t)= dia...

Dynamics of a discrete Lotka-Volterra model

A simple spatiotemporal chaotic Lotka- Volterra model

A mathematically simple example of a high-dimensional (many-species) Lotka-Volterra model that exhibits spatiotemporal chaos in one spatial dimension is described. The model consists of a closed ring of identical agents, each competing for fixed finite resources with two of its four nearest neighbors. The model is prototypical of more complicated models in its quasiperiodic route to chaos (incl...