ON LORENTZIAN SYSTEM OF DIFFERENTIAL EQUATION

 Mohammed Abdullahi, Shuaibu Garba Ngulde and Abba Vulgwe Mandara

Department of Mathematics and Statistics

University of Maiduguri, P. M. B. 1069, Maiduguri, Nigeria

E-mail: abdullahi1960@gmail.com

ABSTRACT

This paper proposes and demonstrates a new integration of the theory of buttery effect of chaos theory in relation to initial conditions. It is very unusual for a mathematical idea to disseminate into the society at large. An interesting example is chaos theory, popularized by Lorenz’s butterfly effect: “does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?” A tiny cause can generate big consequences. We have suggested an analytic approach to Lorentz system and with the use of MACTCONT, toolboxes in MATLAB, we have computed the system using different initial conditions and tracked the behaviuor of the system, eventually ending up by showing impossibility of weather forecasting being ineffective after one week and become chaotic.