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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6410 • ODE

Winter 2004 • Question 3

Question

Math 6410 • ODE Winter 2004 • Question 3

Periodic Orbits. Show that the following translated Fitzhugh-Nagumo system modelling a nerve axon has a nonconstant periodic trajectory in \(\mathbb {R}^2\). \[ \begin {cases} \dfrac {dx}{dt}=0.9x(1-x^2)-y,\\ \dfrac {dy}{dt}=0.5x-0.5y. \end {cases} \]

Raw LaTeX

\textbf{Periodic Orbits.}
Show that the following translated Fitzhugh-Nagumo system modelling a nerve axon has a
nonconstant periodic trajectory in \(\R^2\).
\[
\begin{cases}
  \dfrac{dx}{dt}=0.9x(1-x^2)-y,\\
  \dfrac{dy}{dt}=0.5x-0.5y.
\end{cases}
\]

Topic Tags

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