3. For the second order autonomous differential equation dx dt 2 = x² + 2x + k (a) Find all stationary points in terms of the parameter k = R (b) Find the stability of the stationary points by considering possible ranges of k. (c) What value of k is a bifurcation point? (d) Draw the bifurcation diagram. What type of bifurcation do you see?
3. For the second order autonomous differential equation dx dt 2 = x² + 2x + k (a) Find all stationary points in terms of the parameter k = R (b) Find the stability of the stationary points by considering possible ranges of k. (c) What value of k is a bifurcation point? (d) Draw the bifurcation diagram. What type of bifurcation do you see?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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