Chapter 6.8, Problem 2E

Interpretation Introduction

Interpretation:

To locate the fixed points and calculate the index for the system ${\dot{\text{x}}\text{ = x}}^{\text{2}}\text{, }\dot{\text{y}}\text{ = y}$.

Concept Introduction:

The index of a closed curve $\text{C}$ is an integer that measures the winding of the vector curve $\text{C}$ is an integer that measures the winding of the vector field on $\text{C}$.

The index also provides information about the fixed point that might happen to lie inside the curve.

The index of the closed curve $\text{C}$ can be defined as the net number of counterclockwise revolutions that are made by the vector field.