- #1
lionsgirl12
- 6
- 0
Consider the following system (where B is a real number, B is not equal to 0),
x1' = -2x1 + (B+2)x2
x2' = Bx2
Depending on the value of B, the critical point at (0,0) can be of different type and/or stability. Describe the possible type/stability of the critical point for the different values of B, and give explicitly the corresponding range of values of B in each case.
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My work:
2x2 matrix:
(-2 B+2, 0 B)
This is known as a triangular matrix which means that the eigenvalues are r = -2, B
Since at least one of the eigenvalues are less than 0, we know it is moving directly
toward and will converge to the critical point.
If B is a positive value, then it will be an unstable saddle point.
If B = -2, then it will be an asymptotically stable proper node (or star point).
I am not sure how to determine what B will be.
x1' = -2x1 + (B+2)x2
x2' = Bx2
Depending on the value of B, the critical point at (0,0) can be of different type and/or stability. Describe the possible type/stability of the critical point for the different values of B, and give explicitly the corresponding range of values of B in each case.
-------------------------------------------------------------------------------------------
My work:
2x2 matrix:
(-2 B+2, 0 B)
This is known as a triangular matrix which means that the eigenvalues are r = -2, B
Since at least one of the eigenvalues are less than 0, we know it is moving directly
toward and will converge to the critical point.
If B is a positive value, then it will be an unstable saddle point.
If B = -2, then it will be an asymptotically stable proper node (or star point).
I am not sure how to determine what B will be.