MATH 574 Midterm: MATH574 Winter 2008 Exam

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

Document Summary

Please attempt all questions in the exam booklets provided. No notes, and text books are permitted . This exam of comprises the cover page, and 3 pages of 5 questions. Include the isoclines (nullclines) on your phase portrait. State, without proof, (x0, y0) for all x0 > 0, y0 > 0. What is the ecological signi cance? (c) find a potential hopf bifurcation point for the non-trivial xed point, and show that. Re( d d ) 6= 0 at this point (but do not check the a 6= 0 degeneracy condition). Given that the hopf bifurcation occurs and is supercritical in odell"s model, sketch two plausible phase portraits for close to hopf bifurcation point, one for each side of the bifurcation. What is the ecological signi cance of these phase portraits: de ne the linear stable, linear centre and linear unstable manifolds for a non-hyperbolic xed point.