Unformatted text preview: Hint for 4.3.7: For this problem, the bifurcations occur at μ = 1 , , and -1. Plot phase portraits for μ > 1 , < μ < 1 ,-1 < μ < , and μ <-1 , then sketch a bifurcation diagram that includes both ﬁxed points and singularities (no need to distinguish ﬁxed points from singularities, but be careful to label their stability). What type of bifurcations do you see? Hint for 4.3.8: The bifurcations occur at μ = 1 and -1. Draw phase portraits for μ > 1 ,-1 < μ < 1 , and μ <-1 , then put the ﬁxed points and the singularities into a bifurcation diagram. What do you see?...
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- Spring '10
- Math, SECT, Fixed points, Bifurcations