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 1E
Interpretation Introduction

Interpretation:

Assuming quasi-static approximation N˙0, the first-order equation for n is derived, and N (t) is expressed in terms of n (t), pc is determined when n*=0 becomes unstable for p>pc, type of bifurcation at the laser threshold pc is determined. The range of parameter which makes quasi-static approximation N˙0 is determined.

Concept Introduction:

The first-order equation for the evolution of N(t) can be derived by substituting quasi-static approximation N˙ 0 in the equation N˙ = -GnN - fN +p 

The pump strength can be evaluated by taking derivative of n˙ with respect number of excited atoms n.

Fixed points are the points where n˙ = 0.

The range of parameter for the approximation can be obtained by considering the rate of change of n˙ is very less than the rate of change of N˙

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