Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
Problem 4 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 (e) x = x + tanh(rx) (b) x = rx- (d) - x */* 1+x x * = rx-1+x² x3 (f) * = rx + 1*²²2
Transcribed Image Text:Problem 4 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 (e) x = x + tanh(rx) (b) x = rx- (d) - x */* 1+x x * = rx-1+x² x3 (f) * = rx + 1*²²2
Expert Solution
steps

Step by step

Solved in 6 steps with 5 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS