1. Instabilities in physical systems: Rayleigh-Benard convection. Self focusing and optical solitons. Chemical oscillations. Vegetation patterns.
    2. Mathematical formulation of instabilities: The transcritical, saddle node, pitchfork and Hopf bifurcations. Imperfect bifurcations. Local and global bifurcations. Excitable systems.
    3. Spatio-temporal patterns in small systems. Normal forms and the Center Manifold theorem.
    4. Amplitude equations. Applications to electromagnetic waves in dispersive media, convection, and chemical oscillations. The Non-Linear Shrodinger (NLS) equation, the Newell-Whitehead-Segei (NWS) equation, and the Complex Ginzburg-Landau (CGL) equation.
    5. Phase dynamics. The Eckhaus, zigzag and Benjamin-Feir instabilities. Phase and amplitude turbulence.
    6. Front propagation in bistable systems. Gradient vs. non-gradient systems. The non-equilibrium Ising-Bloch (NIB) bifurcation. Transverse instabilities.
    7. Singular perturbation theory of stationary and traveling patterns in bistable and excitable media.
    8. Spiral waves. Spiral turbulence. Kinematic theory.
    9. Forced oscillations. Frequency locking in spatially extended systems.

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    • There is no one main textbook in the course. Some of the books, which are relevant to the course are listed bellow. The relevant chapters could be read from the table above.

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      • Lecture/Tutorial

        Group What? Name Day Hours Building/Room
        1 Lecture אהוד מרון Tuesday 17:00-20:00 34/014

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            • Grades will be determined by evaluating personal projects to be submitted in a limited period of time.

              A prerequisite for having a grade is the submission of all homework assignments.

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