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