Chapter 12.1, Problem 2E

Interpretation Introduction

Interpretation:

To find the condition on the parameter which ensures that the origin is globally asymptotically stable, where the considered map is the linear map.

Concept Introduction:

• The fixed point of a differential equation is a point where: $\text{f(x*) = 0 ; while substitution f(x*) = }\dot{\text{x}}\text{ is used and x\&*\#x00A0;is a fixed point}$.

• Countable and uncountable sets, where the notion created by a cantor will be followed.

  Different infinite sets can be compared as followed, considering the basis set N as the set of natural numbers; if set A has one - to – one correspondence, i.e., every element in set A can be mapped to one and only one element of set N, then set A is called countable, otherwise it is uncountable.