Some Applications of the Dickson Polynomials of Higher Kind for Modeling Radiation Diagrams

In this paper we consider the Dickson polynomials \(D_{m+1,n}(x,a)\) of the sixth and seven kind (i.e. \(m=5\) and \(m=6\) , respectively). First, a model with Dickson polynomials as corrections in the Lienard system is presented and “level curves” are studied. In the second place, we will note that some specifics of the amplitudes of these high-degree polynomials open up the possibility of modeling signals from the field of antenna-feeder technology. So, for example, changing the variable t by \(t=b\cos \theta +c\) ( \(\theta \) is the azimuthal angle and c is the phase difference) in the y(t)-component of the solution of Lienard differential system results in the generation of radiation diagrams. Numerical examples, illustrating our results using CAS MATHEMATICA are given.