What determines whether a trajectory in a non-linear system moves towards or away from a critical point?

Understanding Non-linear Systems and Critical Points

Interactive Video
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Mathematics, Science
•
11th Grade - University
•
Hard

Lucas Foster
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
The determinant of the Jacobian matrix
The trace of the Jacobian matrix
The sign of the real part of the eigenvalues
The magnitude of the eigenvalues
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the role of the Jacobian matrix in analyzing non-linear systems?
It determines the system's equilibrium points
It helps in linearizing the system around critical points
It provides the solution to the differential equations
It calculates the system's energy
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the given system, what are the eigenvalues at the critical point (0,0)?
1 and -1
3 and -3
0 and 1
0 ± i
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the significance of the eigenvalues being zero plus or minus i at the critical point?
The system is asymptotically stable
The system has a center
The system is a stable node
The system is a spiral sink
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What type of stability is associated with complex eigenvalues having a positive real part?
Stable node
Spiral sink
Spiral source
Center
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does a positive real part of eigenvalues indicate about the system's stability?
The system is stable
The system is unstable
The system is critically stable
The system is neutrally stable
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What happens to the trajectory near the origin when the real part of the eigenvalues is positive?
It oscillates around the origin
It remains at the origin
It spirals towards the origin
It moves away from the origin
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