Dynamics of a discrete Lotka-Volterra model

Dynamics of a discrete Lotka-Volterra model

dynamics and bifurcations of a lotka-volterra population model

this paper investigates the dynamics and stability properties of a discrete-time lotka-volterra type system. we first analyze stability of the fixed points and the existence of local bifurcations. our analysis shows the presence of rich variety of local bifurcations, namely, stable fixed points; in which population numbers remain constant, periodic cycles; in which population numbers oscillate amo...

Dynamically consistent discrete Lotka–Volterra competition systems

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Hamiltonian Dynamics of the Lotka-Volterra Equations

as a model for the competition of n biological species. In this model, xj represents the number of individuals of species j (so Volterra assumes xj > 0), the ajk’s are the interaction coefficients, the εj ’s and the βj’s(> 0) are parameters that depend on the environment. For example, εj > 0 means that species j is able to increase with food from the environment, while εj < 0 means that it cann...

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...