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Chapter 9: Q22E (page 440)

For the linear system x鈫�(t+1)=[30-2.50.5]x鈫�(t) find the matching phase portrait.

Short Answer

Expert verified

The phase portrait corresponds to VII.

Step by step solution

01

To find the eigenvalues

Consider the linear system as follows.

x鈫�t+1=30-2.50.5x鈫�t

To find the eigenvalues, evaluate A-位I=0as follows.

A-位I=03-位0-2.50.5-位=03-位0.5-位-0-2.5=01.5-3位-0.5位+位2-0=0

Simplify further as follows.

位2-3.5位+1.5=0位2-3位-0.5位+1.5=0位位-3-0.5位-3=0位-3位-0.5=0

Simplify further as follows.

位-3=0位1=3位-0.5=0位2=0.5

Therefore, the eigenvalues are 位1=3and 位2=0.5.

02

Observation of the phase portrait

Since, the eigenvalues are 位1=3and 位2=0.5also this shows that, 位1>1>位2>0.

Therefore, the phase portrait is in figure 1 as follows.

Hence, the phase portrait to the linear systemx鈫�t+1=30-2.50.5x鈫�tis VII.

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Most popular questions from this chapter

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