Alex Simmons
New member
Hey,
I'm working with a small set (3) of differential equations for a group project (analysing an Unemployment Model) at Uni (first year). I've figured out the Jacobian or Variation matrix and it's stable at the equilibrium. My question is, can I deduce any more information out of the eigenvalues or possibly the eigenvectors to determine something like 'how stable' the system is, i.e. "if i slightly change the parameters will it become unstable?" etc.
I was thinking something along the lines of that the absolute value of the eigenvalues demonstrates how unstable or stable the system is as the direction from zero determines the stability. I; however, have not been taught this method of analysing stability so I am just purely guessing and would love some more insight as my lack of knowledge is limiting my ability to actually find more information *sad face*. So yea, if i'm completely wrong (so hope i'm not cause i wanna explore this avenue) let me know and i'll try something else otherwise some sources (preferably a good website or two) would be great!
Thanks in advance!
I'm working with a small set (3) of differential equations for a group project (analysing an Unemployment Model) at Uni (first year). I've figured out the Jacobian or Variation matrix and it's stable at the equilibrium. My question is, can I deduce any more information out of the eigenvalues or possibly the eigenvectors to determine something like 'how stable' the system is, i.e. "if i slightly change the parameters will it become unstable?" etc.
I was thinking something along the lines of that the absolute value of the eigenvalues demonstrates how unstable or stable the system is as the direction from zero determines the stability. I; however, have not been taught this method of analysing stability so I am just purely guessing and would love some more insight as my lack of knowledge is limiting my ability to actually find more information *sad face*. So yea, if i'm completely wrong (so hope i'm not cause i wanna explore this avenue) let me know and i'll try something else otherwise some sources (preferably a good website or two) would be great!
Thanks in advance!