Chapter 2.7, Problem 4E

Interpretation Introduction

Interpretation:

To identify all the equilibrium points and their stability for the vector field $\dot{\text{x}}\text{ = 2+sin x}$. To plot the function $\text{V(x)}$.

Concept Introduction:

Potential is $\dot{\text{x}}\text{ = f(x) = -}\frac{\text{dV}}{\text{dx}}$

The points of minima of the function $\text{ V(x)}$ are the stable equilibrium points, and the points of maxima are the unstable equilibrium points.