Chapter 9.6, Problem 4E

Interpretation Introduction

Interpretation:

• a) To show, if $\text{z(t)}$ is used as driver signal receiver doesn’t synchronize the message.

• b) To determine what happens when $\text{y(t)}$ is used as a drive signal.

Concept Introduction:

• ➢ The Lorenz equations are

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

• ➢ The main idea behind the sending the secret message using chaos is while transmitting the message it is masked by louder chaos. The eavesdropping person only hears only chaos, but the receiver perfectly reproduces chaos and subtracts it from the masked message and hears the original message sent by the transmitter.

• ➢ The error dynamics is calculated by

  $\begin{array}{l}{\text{e}}_{\text{1}}=\text{x}-\text{x(t)}\\ {\text{e}}_2\text{= y}-{\text{y}}_{\text{r}}\\ {\text{e}}_{\text{3}}=\text{z}-{\text{z}}_{\text{r}}\\ {\dot{\text{e}}}_{\text{2}}=\dot{\text{y}}-{\dot{\text{y}}}_{\text{r}},\\ {\dot{\text{e}}}_{\text{3}}=\dot{\text{z}}-{\dot{\text{z}}}_{\text{r}},\end{array}$