Basic Elective

Non-Linear Dynamical Systems

CODE
ΜΑΕ204
SEMESTER
7
HOURS per WEEK
3
ECTS CREDITS
5  (Erasmus+ course)
INSTRUCTORS

Georgios Vougiatzis

Foteini Zervaki

·       Introduction to Dynamical systems, analytic and numerical approach - The programming tool "Mathematica"

·       Analytic and Numerical solution of Differential equations with Mathematica

·       Basic notions of the Dynamical systems - Phase space - Classification of systems and trajectories.

·       Conservative systems of one degree of freedom - oscillations

·       Autonomous linear systems 2x2

·       Autonomous nonlinear systems - Stability of equilibrium points and phase space diagrams. Applications (Lotka-Voltera models)

·       Limit cycles. Application to electrical circuit oscillators (Van der Pol)

·       Bifurcations

·       Linear perturbed oscillators – Periodic and quasi-periodic trajectories, limit cycles and Poincare maps.

·       Conservative Oscillators – Poincare maps - Homoclinic chaos.

·       Limit cycles and strange attractor in dissipative Duffing equation

·       Discrete dynamical systems

·       Summary and Discussion

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