II. Let f(n) = ryn(1-Yn) and consider the nonlinear difference equation Yn+1 = f(n) or Yn+1 = ryn(1-Yn) 1. Solve for the two equilibrium points in terms of r. 2. Ifr=1, is the nonzero equilibrium solution stable or unstable? Explain. 3. For what values of r will the nonzero equilibrium be stable?

II. Let f(n) = ryn(1-Yn) and consider the nonlinear difference equation Yn+1 = f(n) or Yn+1 = ryn(1-Yn) 1. Solve for the two equilibrium points in terms of r. 2. Ifr=1, is the nonzero equilibrium solution stable or unstable? Explain. 3. For what values of r will the nonzero equilibrium be stable?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.5: Nonlinear Systems Of Differential Equations

Problem 11E: Whales and Krill For the system of differential equations 10, suppose that F11 and F21. Show that...

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Question

II.
Let f(n) = ryn(1-Yn) and consider the nonlinear difference equation Yn+1 = f(n) or
Yn+1 = ryn(1-Yn)
1. Solve for the two equilibrium points in terms of r.
2. Ifr=1, is the nonzero equilibrium solution stable or unstable? Explain.
3. For what values of r will the nonzero equilibrium be stable?

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