Chapter 10.7, Problem 11E

Interpretation Introduction

Interpretation:

To do cobweb analysis of $\text{f(x})=-(1+\text{μ)x}+{\text{x}}^{\text{2}}$ using initial condition ${\text{μ}}_{\text{1}}\text{=0}$ and show ${\text{μ}}_{\text{k}}\to {\text{μ}}^{\text{*}}$ is a stable fixed point corresponding to onset of chaos, here ${\text{μ}}^{\text{*}}>\text{0}$

Concept Introduction:

• The construction of cobweb map allows to iterate map graphically.

• Cobweb analysis allows seeing global behavior at a glance by supplementing the local information available from linearization. It is the most important process when the linear analysis fails.

• Cobweb diagram shows how flip bifurcation gives rise to period-doubling.