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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6410 • ODE

Fall 2003 • Question 3

Question

Math 6410 • ODE Fall 2003 • Question 3

Periodic Orbits. Show that the following system has a nonconstant periodic trajectory. \[ \begin {cases} \dfrac {dx}{dt}=\bigl [3-\sin (x^2+y^2)\bigr ]y,\\ \dfrac {dy}{dt}=-3x+\cos (x^2+y^2)y. \end {cases} \]

Raw LaTeX

\textbf{Periodic Orbits.}
Show that the following system has a nonconstant periodic trajectory.
\[
\begin{cases}
  \dfrac{dx}{dt}=\bigl[3-\sin(x^2+y^2)\bigr]y,\\
  \dfrac{dy}{dt}=-3x+\cos(x^2+y^2)y.
\end{cases}
\]

Topic Tags

Periodic Orbits, Limit Cycles, and Orbital Stability Poincare Maps and Periodic Solutions