Chapter 5.3, Problem 1E

Interpretation Introduction

Interpretation:

Suggest names for the four romantic styles, determined by the signs of ‘a’ and ‘b’ in $\dot{\text{R}}\text{= aR +bJ}$ .

Concept Introduction:

Eager lover when a>0, b>0.

Narcissistic nerd when a>0, b<0.

Cautious lover when a<0, b>0.

Hermit when a<0, b<0.

Parameter “a” expresses the extent to which Romeo is encouraged by his own feelings, and “b” is the extent to which Romeo is encouraged by Juliet’s feelings.

Answer to Problem 1E

Solution:

For a>0 and b>0 style, Romeo is an Eager lover.

For a>0 and b<0 style, Romeo is a Narcissistic nerd.

For a<0 and b>0 style, Romeo is a cautious lover.

For a<0 and b<0 style, Romeo is a Hermit.

Explanation of Solution

The forecast for lovers is governed by the general linear system

$\dot{\text{R}}\text{= aR+bJ}$

And

$\dot{\text{J}}\text{= cR+dJ}$

Here,

$\dot{\text{R}}$ is Romeo's love if the value of $\dot{\text{R}}$ is positive, and if $\dot{\text{R}}$ is negative, then it’s Romeo's hate. $\dot{\text{J}}$ is Juliet's love if the value of $\dot{\text{J}}$ is positive, and if $\dot{\text{J}}$ is negative, then it’s Juliet's hate The parameter “a” expresses the extent to which Romeo is encouraged by his own feelings, and “b” is the extent to which Romeo is encouraged by Juliet's feelings. The parameter “c” expresses the extent to which Juliet is encouraged by her own feelings, and “d” is the extent to which Juliet is encouraged by Romeo's feelings

The four romantic styles, determined by the signs of a and b as follows:

Eager lover: For $\text{a > 0}$, $\text{b > 0}$

In this romantic style, Romeo is an Eager lover. He gets encouraged by his own feelings. This means that he is encouraged by his own affectionate feelings for her. Also, Romeo gets excited by Juliet’s love for him.

Narcissistic nerd: For $\text{a > 0}$, $\text{b < 0}$

In this romantic style, Romeo is a Narcissistic nerd. He gets excited by his own feelings. This means that he wants more of what he feels. Also, Romeo retreats from the feelings of Juliet. Romeo can also be called flirting fink, who loves to tease than please. Here, Romeo is called a nerd who hates to be loved and loves to be hated.

Cautious lover: For $\text{a < 0}$, $\text{b > 0}$

In this romantic style, Romeo is a cautious lover. He gets encouraged from the feelings of Juliet. This means that Romeo gets excited by Juliet's love for him. He retreats from his own feelings. Romeo can also be called bashful budder. Romeo can be called a secure and synergic lover. This means Romeo suppresses his feelings of love for Juliet when Juliet stops loving him. This romantic style represents the majority of population.

Hermit: For $\text{a < 0}$, $\text{b < 0}$

In this romantic style, Romeo is a Hermit. Romeo retreats from the feelings of Juliet and also retreats from his own feelings. In this style, Romeo does not have the feeling of love.

Conclusion

By using signs of “a” and “b,” one can suggest four different styles for the given linear system.