By using definitions of different types of stabilities, the stabilities of fixed points are to be proved. Concept Introduction: A fixed point x * = 0 is said to be globally attracting, if x * attracts all trajectories in the phase plane. Liapunov Stable: A fixed point is Liapunov stable, if all the trajectories start sufficiently close to x * and remains close to it for all positive time. When a fixed point is Liapunov stable, but not attracting is called neutrally stable. The nearby trajectories are neither attracted nor repelled from neutrally stable points.

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Chapter 5.1, Problem 11E

Interpretation Introduction

Interpretation:

By using definitions of different types of stabilities, the stabilities of fixed points are to be proved.

Concept Introduction:

A fixed point x=0 is said to be globally attracting, if x attracts all trajectories in the phase plane.

Liapunov Stable: A fixed point is Liapunov stable, if all the trajectories start sufficiently close to x* and remains close to it for all positive time.

When a fixed point is Liapunov stable, but not attracting is called neutrally stable. The nearby trajectories are neither attracted nor repelled from neutrally stable points.

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