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?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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?
Transcribed Image Text: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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