17.6 Concluding thoughts

To summarize, let’s say we have the following system of equations

dxdt=f(x,y)dydt=g(x,y)

Assuming we have an equibrium solution at (x,y)=(a,b), the Jacobian matrix at that solution is:

J(a,b)=(fx(a,b)fy(a,b)gx(a,b)gy(a,b))

While we don’t discuss it here, the Jacobian matrix also extends to higher order systems as well.