Chapter 12.4, Problem 3E

Interpretation Introduction

Interpretation:

To obtain a long time series for $\text{x(t)}$ and numerically integrate the Rössler system for $\text{a = 0}\text{.4, b = 2, c = 4}$. By the attractor reconstruction method, plot $\text{(x(t),x(t+τ))}$ for various values of the delay, and find the value of $\text{τ}$ for which the reconstructed attractor looks similar to the actual Rössler attractor. Also, explain how $\text{τ}$ is compared with the typical orbital periods of the system.

Concept Introduction:

• The Rössler system is:

  $\begin{array}{l}\dot{\text{x}}=-\text{y}-\text{z}\\ \dot{\text{y}}=\text{x}+\text{ay}\\ \dot{\text{z}}=\text{b}+\text{z(x}-\text{c})\end{array}$

• In the attractor reconstruction method, the time delay $\text{τ}$ is introduced by observing graphs, for which the value of $\text{τ}$ the phase space looks similar to the actual Lorenz attractor.