CDS - Vector Field

Remember:

Here’s an example of how we can study the geometry of the steady state:

• The black point is a STABLE steady state, also called “attractor”.
• The white point is a UNSTABLE steady state*.
• $\dot{x}$ can also be seen as representig the velocity, as you can see the velocity decreases as you approach the stady state.

There exist particular kinds of vectors, called eigenvectors, that generate all vectors of the vector field.

We have also seen some examples of vector fields for a 2D linear system. And also some examples of vector fields for a 2D non-linear system.

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• eigenvectors ??? and eigenvalues ???TODO

• This is an example of how we can study the geometry of the steady state.
• The black point is a STABLE steady state, also called “attractor”.
• The white point is a UNSTABLE steady state*.
• The arrows define how ???TODO the system evolves / the initial condition evolves
• $\dot{x}$ can also be seen as representig the velocity, as you can see the velocity decreases as you approach the stady state.