MATH 574 Midterm: MATH574 Winter 2010 Exam

• School: McGill University
• Department: Mathematics and Statistics
• Course: MATH 574
• Professor: All

Document Summary

Answer 5 or 6 questions; credit will be given for the best 5 answers. Please attempt all questions in the exam booklets provided. This exam of comprises the cover page, and 2 pages of 6 questions. Math 574: consider the system of di erential equations. X = x xy x(x2 + y2), x(0) = x0 ir, Does the dynamical system have a global attractor, and if it does, what is it: consider a dynamical system de ned by. Label the stable and unstable manifolds of any saddle points. (c) state without proof the -limit sets for all initial conditions. What does this is imply for the animal populations: consider the system of di erential equations. X = 2x + y, x(0) = x0 ir, Hence, determine the value of the parameter ir at which the xed point at (0, 0) is not hyperbolic.