The following nonlinear equations all undergo a bifurcation for some value or values of r. In each case, find these values and the corresponding fixed point x* and classify the bifurcations as saddlenode, transcritical, supercritical pitchfork, or subcritical pitchfork. Finally sketch the bifurcation diagram of fixed points x* vs r, indicating stability of each branch as a solid line for stable fixed points, and a dashed line for unstable fixed points. (a) x=r-3x² (c) * = 5-re-x² x (b) x=rx- 1+x (d) x=rx-- - x 1+x²
The following nonlinear equations all undergo a bifurcation for some value or values of r. In each case, find these values and the corresponding fixed point x* and classify the bifurcations as saddlenode, transcritical, supercritical pitchfork, or subcritical pitchfork. Finally sketch the bifurcation diagram of fixed points x* vs r, indicating stability of each branch as a solid line for stable fixed points, and a dashed line for unstable fixed points. (a) x=r-3x² (c) * = 5-re-x² x (b) x=rx- 1+x (d) x=rx-- - x 1+x²
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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