Chapter 9.4, Problem 1E

Interpretation Introduction

Interpretation:

To compute Lorenz map for $r=28,\sigma =10,b=8/3$ using numerical integration.

Concept Introduction:

• ➢ Lorenz equations

  $\begin{array}{l}\dot{\text{x}}=\sigma (\text{y}-\text{x})\\ \dot{\text{y}}=\text{rx}-\text{y}-\text{xz}\\ \dot{\text{z}}=\text{xy}-\text{bz}\\ \text{Here σ, r, b > 0}\end{array}$

  The solution of Lorenz equations oscillates irregularly for a wide range of parameters, never exactly repeating, but it always remains in a bounded region of phase space.

• ➢ Strange attractor: It is not the same as a fixed point, limit cycle, a point, a curve or surface. It is a fractal having fractional dimensions between $\text{2 and 3}$.

• ➢ Chaos: It is the study of deterministic differential equations that display sensitive dependence on initial conditions.