Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780813349107
Author: Steven H. Strogatz
Publisher: PERSEUS D
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Chapter 3.3, Problem 2E
Interpretation Introduction

Interpretation:

Assuming P˙0, D˙0, the Maxwell–Bloch equations, i.e., first-order equation for the evolution of E is to be derived, where E is the electric field, P is the mean polarization of the atoms, and D is the population inversion. All the fixed points for the equation of E are to be found. The bifurcation diagram of E* vs. λ is to be drawn.

Concept Introduction:

The first-order equation for the evolution of E can be derived by substituting the given conditions in Maxwell–Bloch equations and solving the equations.

Fixed points are the points where E˙ = 0.

Stability can be found by differentiating the derived first order equation with respect to E.

The bifurcation diagram can be drawn using the fixed points.

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