Chapter 12.2, Problem 18E

Interpretation Introduction

Interpretation:

To show numerically, the Lozi map has a strange attractor when $\text{a =1}\text{.7,b = 0}\text{.5}$

Concept Introduction:

• The expressions for the Lozi map are

  ${\text{x}}_{\text{n+1}}{\text{=1+y}}_{\text{n}}-\text{a}\left|{\text{x}}_{\text{n}}\right|,{\text{ y}}_{\text{n+1}}{\text{= bx}}_{\text{n}}$

  Here a and b are real parameters and value of $\text{b}$ belongs the range $\text{-1 < b < 1}$

• Strange attractor means the unlikeness generated by the system with many variables in the chaotic mathematic system. This kind of a pattern is known as the strange attractor.