About the solutions of Modified Lorenz system

Abstract

A Modified Lorenz system is a system of three differential equations. The third differential equation in the Lorenz system is replaced with a fifth-order linear homogeneous differential equation with constant coefficients. In the paper [B. Zlatanovska and D. Dimovski, A modified Lorenz system: Definition and solution, Asian-Eur. J. Math. 13(08) (2020) 2050164], the Modified Lorenz system is defined by offering a solution, but without solving the fifth-order linear homogeneous differential equation with constant coefficients. This differential equation is solved by solving the characteristic equation of fifth degree. A formula for solving the algebraic equation of the fifth degree does not exist. Therefore, solutions for the special cases of the characteristic equation of fifth degree will be offered. The solution of the Modified Lorenz system will be completed using these forms of the characteristic equation of the fifth degree.