For the system of differential equations
x′(t)=−9/5x+5/3y+2xy
y′(t)=−18/5x+20/3y−xy
the critical point (x0,y0) with x0>0,y0>0 is x0= , y0=
Change variables in the system by letting x(t)=x0+u(t), y(t)=y0+v(t). The system for u,v is
u′=
v′=
Use u and v for the two functions, rather than u(t) and v(t)
For the u,v system, the Jacobian matrix at the origin is
A=
⎡⎣⎢⎢⎢ ⎤⎦⎥⎥⎥
You should note that this matrix is the same as J(x0,y0) from the previous problem.
