Problem 1: Consider a two dimensional system .....function.

Problem 1: (22 points) Consider a twodimensional system Li: : f (1:), I E R2 and f is a C1 function. a) Give a short denition for the following notions: hyperbolic xed point closed orbit limit cycle Hopf bifurcation (Problem 1 continued ) b) Give an example of a system that undergoes a Hopf bifurcation. No proof is required. c) Sketch a phase portrait of a system that has a stable limit cycle, a heteroclinc orbit, and a nonlinear center. Sketch some typical trajectories for your system