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nonlinear.dynamics.and.applications
.to.engineering.systems
NTUA, Inter-Departmental
Postgraduate Program "Mathematical Modeling in Modern Technologies
and Finance"; 2003-2006
From the simplicity of the linear to the complexity of nonlinear
systems. Flows in phase-space, steady and transient behaviour, stationary
solutions and periodic orbits, multiplicity of solutions, analysis
of stability. Attractors and their basins of attraction. Invariant
manifolds. Poincaré maps, Floquet theory. Limitations of
perturbation methods for strongly nonlinear systems. Parametric
investigation of steady-state solutions of nonlinear systems. Local
bifurcations (fold, flip, pitchfork, Hopf) and their qualitative
characteristics. Analytical and numerical methods for the study
of bifurcations. Imperfect bifurcations. Co-dimension and “structural
stability”. Global bifurcations and their importance for the
safety of engineering systems. Problems of instability of ships
in waves. Derivation of simplified models (model reduction) for
complex dynamical systems. The concept of chaos for a regularly
excited nonlinear dynamical system. Strange attractors, sensitive
dependence on initial conditions, loss of predictability. Transition
to chaotic behaviour. Fractal dimension and self-similarity. Implications
for the design and operation of engineering systems.
Co-instructors: Prof. K. Spyrou and Assoc. Prof. I. Georgiou
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