NUMERICAL RESULTS FOR LOTKA-VOLTERRA MODEL USING APPROXIMATE INERTIAL MANIFOLDS

A numerical study on the classical Lotka-Volterra model is performed, using approximate inertial manifolds. An analytical study consisting in the inertial form of the system is made. The construction of the approximate inertial manifolds is based on the identification of the absorbing domains using the graphical representations of the phase portraits. The hypotheses of the Jolly-Rosa-Temam algorithm are verified for certain values of parameters and the approximate inertial manifolds are constructed. Errors of approximation are computed.

Uniform Attractor and Approximate Inertial Manifolds for Nonautonomous Long-Short Wave Equations

Nonautonomous long-short wave equations with quasiperiodic forces are studied. We prove the existence of the uniform attractor for the system by means of energy method, which is widely used to deal with problems who have no continuity (with respect to the initial data) property, as well as to those which Sobolev compact imbedding cannot be applied. Afterwards, we construct an approximate inertial manifold by means of extending phase space method and we estimated the size of the corresponding attracting neighborhood for this manifold.