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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6410 • ODE

Spring 2011 • Question 5

Question

Math 6410 • ODE Spring 2011 • Question 5

Determine whether the planar system \[ \begin {aligned} \dot {x} &= x-x^3-xy^2,\\ \dot {y} &= 2y-y^5-yx^4 \end {aligned} \] has any nonconstant periodic solutions.

Raw LaTeX

Determine whether the planar system
\[
\begin{aligned}
  \dot{x} &= x-x^3-xy^2,\\
  \dot{y} &= 2y-y^5-yx^4
\end{aligned}
\]
has any nonconstant periodic solutions.

Topic Tags

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