Lorenz’s system - analysis of a sensitive system
Edward Lorenz, butterfly effect
Meteorology is a branch of geophysics concerned with atmospheric processes and phenomena and atmospheric effects on our weather. Edward Lorenz was a devoted meteorologist who made several significant contributions to this field. We first describe the fascinating history of Lorenz’s discoveries and his revolutionary additions to the area of meteorology. In particular, he noted the extremely sensitive dependence on the initial conditions of a Chaotic system in the atmosphere, which is commonly referred to as the Butterfly Effect and pertains to Lorenz’s system of three Ordinary Differential Equations (ODEs) that models the atmospheric convection in the atmosphere. We conducted a novel, in-depth mathematical analysis of the Theorem of Existence and Uniqueness for a system of ODEs in general and addressed how it applies to Lorenz’s system. Further, we exhibited how Lorenz’s system is ill-posed using an application where we varied the initial parameters by minimal variations and noted relatively quick and drastic differences in the trajectories of the system.
All Rights Reserved