T13.2 The graph below shows the graph of the function f(x) = dx/dt. (a) Draw a p

Question

T13.2 The graph below shows the graph of the function f(x) = dx/dt. (a) Draw a phase line diagram for the dynamical system specified by dx/dt. (b) What are the equilibrium states of this system? (c) Which of these equilibria are stable and which are unstable?

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                                    -2         -1        0         1             2         3

T13.2 Consider the dynamical system given by dw/dt = cos(5 w). (a) Find the equilibria w* of the system that satisfy 0?w*?4. (b) Find the stability of those equilibria. (c) Draw a phase line diagram for this system.

T13.3 Consider the disease example: dI dt =?I (1? I )??I (a) Find the conditions on ? and ? that determine when the equilibrium at I=0 is stable or unstable. (b) Write out the meaning of this condition in words as interpreted in the model that underlies the meaning of the two parameters. (c) What happens to the other equilibrium value when the equilibrium at I=0 is stable?

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Explanation / Answer

www.scribd.com/doc/50357722/Vibrations

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