Chapter 9.2, Problem 3E

Interpretation Introduction

Interpretation:

To show that all trajectories eventually enter and remain inside a large sphere S of the form ${\text{x}}^{\text{2}}{\text{ + y}}^{\text{2}}\text{ + }{\left(\text{z - r - σ}\right)}^{\text{2}}\text{ = C}$, for a sufficiently large C.

Concept Introduction:

• ➢ The Lorenz equations are given as

  $\dot{\text{x}}=\text{σ}\left(\text{y - x}\right)$,

  $\dot{\text{y}}=\text{rx - xz - y}$,

  $\dot{\text{z}}=\text{xy - bz}$

  Here, $\text{σ, r, b > 0}$.