NUMERICAL RESULTS FOR LOTKA-VOLTERRA MODEL USING APPROXIMATE INERTIAL MANIFOLDS

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...

A Perturbation Approach for Approximate Inertial Manifolds

We present an explicit form for the construction of approximate inertial manifolds (AIMs) for a class of nonlinear dissipative partial differential equations by using a perturbation technique. We investigate two numerical examples of the reaction diffusion equation with polynomial nonlinearity and non-polynomial nonlinearity to show comparison of accuracy for our perturbation method with other ...

Dynamic Optimization of Dissipative PDE Systems Using Approximate Inertial Manifolds

Abstract In this work, we propose a computationally efficient method for the solution of dynamic constraint optimization problems arising in the context of spatiallydistributed processes governed by highly-dissipative nonlinear partial differential equations (PDEs). The method is based on spatial discretization using combination of the method of weighted residuals with spatially-global basis fu...

Dynamics of a discrete Lotka-Volterra model