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all classes   first 8 weeks   second 8 weeks   EMB 2/03-5/20   evenings (4pm and later)

AE 554
Dynamical Systems Theory

Credit:  4 hours.


Fundamental concepts of nonlinear oscillations, structural stability, local and global bifurcations in the context of ordinary and partial differential equations; introduction to dynamic systems, structural stability and Lyapunov-Schmidt Reduction, bifurcations of equilibrium points, limit cycles and tori, the center manifold and Poincare normal forms, co-dimension two and higher order bifurcations, bifurcation theory of maps, the Birkhoff-Smale homoclinic theorem and horseshoes, Melnikov's method and Silnikov phenomena, period doubling, and other routes to chaos. Applications to many engineering problems, such as aircraft at high angles of attack, pipes conveying fluid, and panel flutter will be demonstrated. Prerequisite: AE 352 or TAM 412.