Question:

dx/dt = x - y + (x^2) - xy

dy/dt = -y + (x^2)

- Determine the critical points for the equation,

- Determine the linearized system for each critical point and discuss whether it can be used

to approximate the behaviour of the non-linear system. What is the type and stability of

each critical point?

Answer:

Hey guys! First post, hope all goes well and there will me many more to come

Ok I am doing this problem and this is the first time I've come across non-linear first order ODE's, usually I have been doing linear ones!

Basically I have established the critical points occur at (0,0) and (1,1) from:

Critical points occur when:

dx/dt = 0 and dy/dt = 0

I am not sure at all how to determine the linearized system for each critical point. I have looked in a couple of text books and online but havent found too much unfortunately.

Any advice on how to go about this step would be great. If anyone knows of a good place to find an worked example of a similar question that would be great too (I have found this is the best way for me to learn, personally works really well for me!)

Thanks in advance