· 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)
· 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