WILL WARD

This exercise is from Nonlinear Dynamics and Chaos, 2nd Edition by Steven H. Strogatz

• Part 1: One-Dimensional Flows

  • 2 Flows on the Line

Exercise 2.2.3
Analyze the following equation graphically. Sketch the vector field on the real line, find all the fixed points, classify their stability, and sketch the graph of $x(t)$ for different initial conditions. Then try to obtain the analytical solution for $x(t)$.

$\dot {x} = x - x^{3}$

From the above graph of $\dot {x} = x - x^{3}…$