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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6410 • ODE

Spring 2013 • Question 5

Question

Math 6410 • ODE Spring 2013 • Question 5

Show that the planar system \[ \begin {aligned} \dot {x} &= x(x^2+y^2-3x-1)-y,\\ \dot {y} &= y(x^2+y^2-3x-1)+x \end {aligned} \] has at least one nonconstant periodic solution.

Raw LaTeX

Show that the planar system
\[
\begin{aligned}
  \dot{x} &= x(x^2+y^2-3x-1)-y,\\
  \dot{y} &= y(x^2+y^2-3x-1)+x
\end{aligned}
\]
has at least one nonconstant periodic solution.

Topic Tags

Distributions and Weak Solutions Entropy Solutions, Shocks, and Rarefactions Periodic Orbits, Limit Cycles, and Orbital Stability Poincare Maps and Periodic Solutions