On a Hypothetical Model with Second Kind Chebyshev’s Polynomial–Correction: Type of Limit Cycles, Simulations, and Possible Applications

Abstract

In this article, we explore a new extended Lienard-type planar system with “corrections” of the second kind Chebyshev’s polynomial Un. The number and type of limit cycles are also studied. The discussion on the y(t)—component of the solution of the Lienard system is connected to searching for the solution of the synthesis of filters and electrical circuits. Numerical experiments, depicting our outcomes using CAS MATHEMATICA, are presented.

Keywords

• Lienard system
• Melnikov’s approach
• corrections of polynomial type
• second kind Chebyshev’s polynomial <i>U_n</i>
• extended generalized oscillator model
• adaptive filter