DYNAMICS OF THE LIENARD SYSTEM USING CONTINUOUS AND BIVARIATE q–HERMITE POLYNOMIALS. SOME APPLICATIONS

Abstract

In this article we consider continuous q–Hermite polynomials generatedby relation Hm+1(x; q) = 2xHn(x; q)−(1−qn)Hn−1(x; q); H0(x; q) = 1; H−1(x; q) = 0and bivariate q–Hermite polynomials generated by relation Hm+1(x, s, q) = xHn(x, s, q)−(1 − qn)sHn−1(x, s, q); H0(x, s, q) = 1; H1(x, s, q) = x with possible applications intwo directions – the study the dynamics of differential systems and the generation ofspecial classes of radiation diagrams. Numerical examples, illustrating our results usingCAS MATHEMATICA are given.