Suppose x, is the size of a population in generation t and in generation t + 1, X1 = f(x,), where f'(x) > 0 for x 2 0. Suppose there are exactly three hyperbolic equilibria given by i = 0, 2, 4. X1 = S(x,) 4 (a) The graph in Figurc 2.19 is the reproduction curve y f(x) or x,= f(x,) and the line y =x or x,+1 = x,. Detcrmine the local stability of cach of the threc equilibria by noting the slope at each of the equilibria.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Suppose x, is the size of a population in generation i and in generation t + 1,
X = f(x,),
where f'(x) > 0 for x 2 0. Suppose there are exactly three hyperbolic cquilibria
given by i = 0, 2, 4.
X+1
X11= S(x,)
2
(a) The graph in Figure 2.19 is the reproduction curve y = f(x) or x, = f(x,)
and the line y = x or x,+1 = x,. Detcrmine the local stability of cach of the
threc equilibria by noting the slope at each of the equilibria.
Transcribed Image Text:Suppose x, is the size of a population in generation i and in generation t + 1, X = f(x,), where f'(x) > 0 for x 2 0. Suppose there are exactly three hyperbolic cquilibria given by i = 0, 2, 4. X+1 X11= S(x,) 2 (a) The graph in Figure 2.19 is the reproduction curve y = f(x) or x, = f(x,) and the line y = x or x,+1 = x,. Detcrmine the local stability of cach of the threc equilibria by noting the slope at each of the equilibria.
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