Transient Chaos in the Lorenz Equations

Abstract

This project provides a study into transient chaos in the Lorenz system. Transient chaos occurs in the parameter region 13.926 smaller to equal to less than 24.06 and the lifetime of trajectories were found to increase exponentially as 𝑟 = 24.06 was approached. The sensitivity to initial conditions was tested by generating random coordinates to be used as initial states of the Lorenz system. The lifetimes of the chaotic transients from these states also increased exponentially towards 𝑟 = 24.06. Transiently chaotic trajectories were found to decay exponentially by means of a subcritical Hopf bifurcation. The decay time increases towards 𝑟 = 24.06 but the final decay was found to not be dependent upon the initial state.

Date of Award	19 Jul 2016
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Thomas Mullin (Main Supervisor)