dynamics and bifurcations of a lotka-volterra population model

Dynamics of a discrete Lotka-Volterra model

Modeling Population Dynamics with Volterra-Lotka Equations

The purpose of this project is to model multi-species interactions using Volterra-Lotka equations in both two and three dimensions. Changes in population dynamics that arise as a result of modifying parameters are examined. The population dynamics of the resulting systems are analyzed in terms of stability around equilibrium points and within invariant surfaces. Of particular interest is period...

Lotka-Volterra population model of genetic evolution

A deterministic model of an age-structured population with genetics analogous to the discrete time Penna model [1, 2] of genetic evolution is constructed on the basis of the Lotka-Volterra scheme. It is shown that if, as in the Penna model, genetic information is represented by the fraction of defective genes in the population, the population numbers for each specific individual's age are repre...

Population Dynamics of Stochastic Lattice Lotka–Volterra Models

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...