MATH 251 Final: MATH 251 PSU C251Final(sp05)
Document Summary
Answer key: consider the following nonlinear system of ode"s, 2pt determine its critical points. Factoring gives x = x xy y = xy 2y gives two critical points x0 = 0. 1 !: 10pt approximate this nonlinear system near each one of its critical points by a linear system of ode"s. State the type and stability of the critical point of approximating linear system. At 0 which has eigenvalues r1 = 1 and r2 = 2, opposite signs. Hence the origin is a saddle for for this system, which is unstable, and the system has trajectories along the x-axis moving towards the origin and trajectories along the y-axis moving away the origin. Substituting this into the original equation gives u = x 2 v = y 1 u = (u + 2)v 2v v = (v + 1)( u) u. The eigenvalues of this system 2 are purely imaginary.
