Numerical analysis of behavior for Lorenz system with Mathematica

Abstract

In this paper will be given numerical analyses of the Lorenz system with the method Runge-Kuta. The method Runge-Kuta is numerical method and it does not give precise analysis, but in absence of the explicit solutions for the Lorenz system, it can be a good method for analysis . We will give intervals for t, where the system converges to a fixed point or there is a chaos but is not so precise assessment. The analysis will be made by changing the parametars sigma, r, b so that: we will change one parametar and two others remain fixed, wi will change two parametars and the third remains fixed or we will change all three parametars in the parametric space (sigma,r,b). Numerical analysis of the system was maid with mathematical package Mathematica.