Not offered in the academic year 2024-2025
- 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 2×2
- 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
