Chapter 9.1, Problem 3E

Interpretation Introduction

Interpretation:

To find the change of the variables that convert the waterwheel equations to the Lorenz equations.

To show that when waterwheel equations are translated into the Lorenz equations, the Lorenz parameter b becomes $\text{b = 1}$.

Concept Introduction:

• ➢ The fixed point of a differential equation is a point where $\text{f(x*) = 0 ; while substitution f(x*) = }\dot{\text{x}}\text{ is used and x\&*\#x00A0;is a fixed point}$.

• ➢ The Lorenz system is the system of the ordinary differential equations which have a chaotic solution for the particular parameter values and initial conditions.