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6 Nov 2019
In the problems below, the coecient matrix contains a parameteralpha. For both of these
matrices, carry out the following steps.
(i) Determine the eigenvalues in terms of alpha.
(ii) Find the critical value or values of alpha where thequalitative nature of the phase
portrait for the system changes.
(iii) Draw a phase portrait for a value of alpha slight below,and for another value slightly
above, each critical value.
(iv) Draw a phase portrait when alpha is exactly the criticalvalue.
a. x'=[alpha 1] b.x'=[-1 alpha]
[-1 alpha] x [-1 -1] x
In the problems below, the coecient matrix contains a parameteralpha. For both of these
matrices, carry out the following steps.
(i) Determine the eigenvalues in terms of alpha.
(ii) Find the critical value or values of alpha where thequalitative nature of the phase
portrait for the system changes.
(iii) Draw a phase portrait for a value of alpha slight below,and for another value slightly
above, each critical value.
(iv) Draw a phase portrait when alpha is exactly the criticalvalue.
a. x'=[alpha 1] b.x'=[-1 alpha]
[-1 alpha] x [-1 -1] x
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