Section 4 exercises: Linear systems in 2 dimensions

Complete these as you are going through part 4. Try and do questions from this regularly. These questions are taken from Nonlinear Dynamics and Chaos by Strogatz.
1
.
For the following differential equations, calculated the eigenvalues and eigenvectors of the eigenvalue equations, plot the phase portraits and classify the systems. (Answers)
​
1
.

x
=y,

y
=-2x-3y
2
.

x
=5x+10y,

y
=-x-y
3
.

x
=3x-4y,

y
=x-y
4
.

x
=-3x+2y,

y
=x-2y
5
.

x
=5x+2y,

y
=-17x-5y
6
.

x
=-3x+4y,

y
=-2x+3y
7
.

x
=4x-3y,

y
=8x-6y
8
.

x
=y,

y
=-x-2y
​
​
2
.
What will Thando and Marsha’s future be in the following situations?
1
.

T
=M,

M
=-T+M
2
.

T
=aM,

M
=bT(foranyrealaandb)
3
.

T
=aT+bM,

M
=-bT-aM
4
.

T
=aT+bM,

M
=bT+aM.Whatifa=b?
5
.

T
=0,

M
=aT+bM
Homepage

​​JonathanShock,UniversityofCapeTown2021​​jon.shock@gmail.com