Chapter 12.3, Problem 1E

Interpretation Introduction

Interpretation:

To explore the Rossler system numerically. Fix $\text{b=2}$, $\text{c=4}$, and increase $\text{a}$ in small steps from $\text{0 to 0}\text{.4}\text{.}$

1. To find the approximate value of $\text{a}$ at the Hopf bifurcation and at the first period-doubling bifurcation.

2. To plot the attractor for each $\text{a}$ and plot time series $\text{z(t)}$.

Concept Introduction:

• The Rossler system is expressed by the following expressions,

  $\dot{\text{x}}\text{=}\text{}\text{}\text{-}\text{}\text{y}\text{}\text{-x}$

  $\dot{\text{y}}\text{=}\text{}\text{}\text{x}\text{}\text{+}\text{ay}$

  $\dot{\text{z}}\text{=}\text{}\text{}\text{b}\text{}\text{+}\text{z(x}\text{-}\text{c)}$

  Here, $\text{a}\text{b}\text{and}\text{c}$ is the control parameter.