Chapter 4.5, Problem 3E

Interpretation Introduction

Interpretation:

The system $\dot{\text{θ}}\text{ = μ + sinθ}$ satisfies two properties: $1)$ it has a unique, globally attracting rest state, and $2)$ a large enough stimulus can send the system on a long excursion through phase space before it returns to the resting state is to be showed and $\text{V(t)}$ for various initial conditions is to be sketched if $\text{V(t) = cosθ(t)}\text{.}$

Concept Introduction:

Fixed points are the points where $\dot{\text{x}}\text{ = 0}$.

If the flow is towards the right $\dot{\text{x}}\text{ > 0}$ and if it is towards left $\dot{\text{x}}\text{ < 0}$, $\dot{\text{x}}\text{ = 0}$ represents no flow.

Stable points are points at which the local flow is toward them.

Unstable points are points at which the local flow is away from them.