Course Outline

Course Outline - ME 680: BIFURCATIONS AND CHAOS (Spring...

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1 ME 680: BIFURCATIONS AND CHAOS (Spring 2010) Instructor: Anil K Bajaj, School of Mechanical Engineering, Office: Room ME 368 (Alternatively, Room ME 110): Phone # 494-6896. Time and Place: Tuesday, Thursday: 1:30 pm - 2:45 pm, Room ME 256. Text Book: (1) Troger, H. and Steindl, A.: Nonlinear Stability and Bifurcation Theory: An Introduction for Scientists and Engineers, Springer-Verlag, Wein, 1991. + Class Notes. Prerequisite: ME 580 or equivalent, or consent of instructor/ an appreciation of analysis of mathematical models and some mathematical maturity. Objective: The course is intended to introduce and develop an understanding of the concepts in nonlinear dynamical systems and bifurcation theory , and an ability to analyze nonlinear dynamic models (given by ordinary as well as partial differential equation descriptions) of physical systems for their dependence on system or control parameters. These include the recent developments in irregular motions and chaos in dissipative systems. The emphasis is to be on understanding the underlying basis of local bifurcation analysis techniques and their applications to structural, mechanical, thermo-mechanical, aeroelastic and chemical systems. Grading: Course grade will be based on some home assignments, seminar presentations prepared on the basis of assigned topics from literature, a class project with final presentation and report. OUTLINE 1. Introduction: Examples of nonlinear behavior in structural, fluid-mechanical and chemical/biological systems. 2. Review of First-Order Nonlinear ODE:
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Course Outline - ME 680: BIFURCATIONS AND CHAOS (Spring...

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