Math 308 - Differential Equations Fall 2002
Homework Assignment 4
Due Friday, October 4.
1. Consider the differential equation
dy
dt =y(y2+µy + 1).
The equation contains a parameter µ.
You can use Maple to create the graphs in this problem (but you don’t have to).
(a) For each of the following values of µ, (i) sketch the graph of dy
dt vs. y, (ii) find and classify the
equilibria, and (iii) sketch the phaseline:
µ=−2.5, µ =−1, µ = 1,and µ= 2.5.
(b) Determine the bifurcation values of µ, and describe the change in qualitative behavior of the
solutions at each bifurcation value.
(c) Sketch of bifurcation diagram. That is, make a plot of the yvalues of the equilibria versus µ.
(Examples of bifurcation diagrams are shown in Figures 1.81. 1.83, and 1.88 in the text.)
Text Problems:
•Section 1.7/ 2, 12
•Section 1.8/ 2, 3, 6, 10, 14, 26
Note: Reread pages 104–107 before starting 1.7/12.
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