Qualitative properties of a cooperative degenerate Lotka-Volterra model

Qualitative Analysis for A Lotka-Volterra Model with Time Delays

This paper considers a Lotka-Volterra model with time delays and delay dependent parameters. The linear stability conditions are obtained with characteristic root method. The Hopf bifurcation is demonstrated. Using normal form theory and center manifold theory, Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions are derived. Finally,...

A Two-Species Cooperative Lotka-Volterra System of Degenerate Parabolic Equations

and Applied Analysis 3 where fM sup{f x, t | x, t ∈ Ω × }, fl inf{f x, t | x, t ∈ Ω × }, we show that the generalized solution is uniformly bounded. At last, by the method of monotone iteration, we establish the existence of the nontrivial periodic solutions of the system 1.1 1.2 , which follows from the existence of a pair of large periodic supersolution and small periodic subsolution. At last...

Dynamics of a discrete Lotka-Volterra model

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...

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...