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Apr 18, 2024
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MATH 721 - Nonlinear Dynamics and Chaos I (3 units)
Geometric approach to nonlinear dynamics, Poincare maps, center manifolds, normal forms, averaging method.
Units of Lecture: 3
Student Learning Outcomes
Upon completion of this course, students will be able to:
1. demonstrate an advanced level of competency in geometric approach to 1 and 2- dimensional flows, stability analysis, Lyapunov stability and Lyapunov function method, classification and analysis of bifurcation of equilibria in 1 and 2-dimentional flows, conservative, reversible and dissipative systems, index theory.
2. demonstrate an advanced level of competency in application of Poincare-Bendixon theorem, Lienard system, Hopf bifurcations, global bifurcation of cycles, hyperbolic systems.
3. demonstrate an advanced level of competency in asymptotic methods, weakly coupled nonlinear oscillators, synchronization phenomena in nonlinear systems and real world models.
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