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Bilkent University

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Undergraduate and Graduate Programs 2020-2021

MATH 344 Introduction to Dynamical Systems

Systems oflinear differential equations, phase portraits. Nonlinear equations. Existence and uniqueness theorems. Flows and limit sets. Equilibrium and periodic solutions. Local stability and the linearization principle. Global stability and the Liapunov method. Planar systems and the Poincaré-Bendixson theorem. Invariant manifolds. Bifurcations. Discrete dynamical systems. Strange attractors and chaos. Numerical methods. Applications in biology, mechanics, and engineering. Credit units: 3 ECTS Credit units: 5, Prerequisite: MATH 223 and MATH 240.

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