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Chapter 9: Q15E (page 439)

Consider a noninvertible 2脳2matrix A with a positive trace. What does the phase portrait of the systemdx鈫�/dy=Ax鈫�look like?

Short Answer

Expert verified

The phase portrait of the systemdx鈫�/dy=Ax鈫� look like asymptotically stable

Step by step solution

01

Step 1:Explanation for the phase of the system dx→/dy=Ax→

Consider a noninvertible 2脳2matrix A with a positive trace.

Where A is a real2脳2matrix.

Then the zero state is an asymptotically stable equilibrium solution if and only if trA<0and detA>0

02

Explanation for the phase of the system dx→/dy=Ax→

Here is the phase looks like asymptotically stable.

位1,2=p卤iq

p2+q2=1位1,2=卤iq

The phase portrait of the system dx鈫�/dy=Ax鈫�look like asymptotically stable.

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Most popular questions from this chapter

Solve the differential equationf''(t)-9f(t)=0and find all the real solutions of the differential equation.

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If the systemdx鈫�dt=Ax鈫�is stable, isdx鈫�dt=A-1x鈫�stable as well? How can you tell?

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Question: Solve the system

dx鈫�dt=Ax鈫�

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1. Finde2蟺i .
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