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  • Course Information
    • Course Title Code Semester Laboratory+Practice (Hour) Pool Type ECTS
    Nonlinear Dynamical Systems MATH409 FALL-SPRING 3+0 E 6
    Learning Outcomes
    1-Solves linear or decoupled system of ODEs
    2-Calculates fixed points or periodic orbits of systems
    3-Sketches the phase portraits
    Prerequisites -
    Language of Instruction English
    Responsible Dr. Harun BALDEMİR
    Instructors -
    Assistants -
    Resources R1 - Strogatz, S. H. (2018). Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. CRC Press. R2 - Lecture Notes
    Supplementary Book SR1 - Ermentrout, B. (2002). Simulating, analyzing, and animating dynamical systems: a guide to XPPAUT for researchers and students. Society for Industrial and Applied Mathematics. SR2 - Lynch, S. (2004). Dynamical systems with applications using MATLAB. Boston: Birkhäuser.
    Goals This course aims to introduce the main features of dynamical systems as models in applied marthematics.
    Content ODEs and dynamical systems, XPPAUT, MATLAB/Octave, 1 dimensional flows, fixed points, stability, linear stability analysis, existence and uniqueness, numerical methods, bifurcation theory, saddle-node bifurcation, transcritical bifurcation, pitchfork bifurcation, cusp catastrophe, flows on circle, 2 dimensional flows, classification of linear systems, phase plane analysis, limit cycles, bifurcations in 2D systems, Hopf bifurcation, quasi-periodicity, Poincare maps
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