Math Economics

Suppose the nonlinear system dx/ dt = f(x,y), dyldt = g(x, y) has a fixed point at (x*, y*). Derive the linearisation of the system about (x* ,J* ) . Show that the system dx dy dt = X-xy, = xy - y dt has two fixed points and find the linearisation of the system about each fixed point. Determine the nature of each fixed point and discuss briefly the implications of this information for the solution paths of the nonlinear system