SOME INVESTIGATIONS AND SIMULATIONS ON THE PLANAR RAYLEIGH–LIENARD DIFFERENTIAL SYSTEM (WEB PLATFORM UPGRADE)

Abstract

In this article we demonstrate some specialized modules for investi-dygating the dynamics of the planar Rayleigh–Lienard differential system dxdt = y; dt =−P oly(x) + ǫF (x, y)y, an integral part of a planned much more general Web–basedapplication for scientific computing. The polynomials P oly(x) as ”corrections”, can bearbitrary orthogonal polynomials and their associated polynomials. The Web–basedapplication, with the ability to upgrade and include additional modules that existingplatforms (with paid and free access) do not provide to users (for example, modulesfor automatic generation of theorems for the number and type of limit cycles (in thelight of Melnikov’s considerations), generation of radiation diagrams, etc.) Numericalexamples, illustrating our results using CAS MATHEMATICA are given.