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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6410 • ODE

Spring 2018 • Question 5

Question

Math 6410 • ODE Spring 2018 • Question 5

Consider Rayleigh’s equation \[ \ddot {x}+\dot {x}^3-2\mu \dot {x}+x=0. \] What kind of bifurcations occur to the equilibrium point of system as the parameter \(\mu \) is varied? Determine the bifurcation values and describe how the solutions change near the bifurcation point.

Raw LaTeX

Consider Rayleigh's equation
\[
  \ddot{x}+\dot{x}^3-2\mu\dot{x}+x=0.
\]
What kind of bifurcations occur to the equilibrium point of system as the parameter
\(\mu\) is varied? Determine the bifurcation values and describe how the solutions
change near the bifurcation point.

Topic Tags

Bifurcation Theory Distributions and Weak Solutions Phase Plane Analysis Poincare Maps and Periodic Solutions