Fundamental Theory: Existence and Uniqueness Theorems for Solutions: Picard s Theorem, Peano s Theorem. Extensibility of Solutions. Differentiability of Solutions. Continuous Dependence on Initial Data and Parameters. Gronwall s Inequality. Stability: Introduction. Autonomous Systems. Stability of Linear Systems: General Theory, Autonomous. Linear Systems in the Plane. Stability of Almost Linear Systems: Linearization. Lyapunov s Method. Center Manifold Theorem. Algebraic Stability Criteria. Periodic Solutions: Floquet Theory. Poincare-Bendixson Theorem, Applications. Stability of Periodic Solutions. Periodic Solutions for Non-Autonomous Systems. Applications: Oscillator Equation. Van der Pol Equation. Mathieu Equation. Hill Equation. Lienard Equation. Bifurcation Theory: Introductory concepts. Elementary Examples. Poincare – Andronov – Hopf Bifurcation. Applications.
- Teacher: Ιάσων Καραφύλλης
ECTS : 5
Language : el