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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6410 • ODE

Fall 2013 • Question 5

Question

Math 6410 • ODE Fall 2013 • Question 5

Consider a modified predator-prey model in the first quadrant. Show that it has at least one nonconstant periodic solution. \[ \begin {aligned} \dot {x} &= x(8-x)-\frac {9xy}{x+1},\\ \dot {y} &= y\left (1-\frac {y}{x}\right ) \end {aligned} \]

Raw LaTeX

Consider a modified predator-prey model in the first quadrant. Show that it has at
least one nonconstant periodic solution.
\[
\begin{aligned}
  \dot{x} &= x(8-x)-\frac{9xy}{x+1},\\
  \dot{y} &= y\left(1-\frac{y}{x}\right)
\end{aligned}
\]

Topic Tags

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