Overview
Description
Geometric approach to nonlinear dynamics, Poincare maps, center manifolds, normal forms, averaging method.
Units
Lecture3
Learning Outcomes
- 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.
- demonstrate an advanced level of competency in application of Poincare-Bendixon theorem, Lienard system, Hopf bifurcations, global bifurcation of cycles, hyperbolic systems.
- demonstrate an advanced level of competency in asymptotic methods, weakly coupled nonlinear oscillators, synchronization phenomena in nonlinear systems and real world models.