Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780813349107
Author: Steven H. Strogatz
Publisher: PERSEUS D
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Chapter 8.1, Problem 15E
Interpretation Introduction

Interpretation:

To interpret and justify the form of various terms in the equations n˙A = (p + nA)nAB - nAnB, n˙B = nBnAB - (p + nA)nB, where nAB = 1 - (p + nA) - nB. If nB(0) = 1 - p, and nA(0) = nAB(0) = 0, to numerically integrate the system until it reaches equilibrium. To show that the final state changes discontinuously as a function of p. To show analytically that pc = 1 - 320.134. To find the type of bifurcation occurs at pc.

Concept Introduction:

  • Fixed points occur where n˙A = 0, and n˙B = 0.

  • Linearization

    A = (n˙AnAn˙BnAn˙AnBn˙BnB)

  • The Eigenvalue λ can be calculated using the characteristic equation

    |(A - λI)| = 0

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