CAAM 435, DYNAMICAL SYSTEMS


Instructor: Yuri Dabaghian
dabaghian@rice.edu
DH 2006
(713) 348-6073

 
Course materials: Syllabus

 
Lecture schedule:
 
Mon - Wed - Fri 2pm, Duncan Hall 1061
Office hours: Duncan Hall 2006, Mon 3-5 pm, Wed and Fri by appointment.

 
Recommended Prerequisites:
 
  • CAAM 210 and MATH 212,
  • CAAM 335 or MATH 355,
  • CAAM 401 or MATH 321.
    		•

     
    Primary Textbook:
     
    S. Strogatz, Nonlinear dynamics and chaos : with applications to physics, biology, chemistry, and engineering, Perseus Books, 1994.
    E.M. Izhikevich, Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. The MIT press, 2007. Chapter 3, "One-Dimensional Systems".
    Reference Texts: D. K. Arrowsmith and C. M. Place, Dynamical Systems: Differential Equations, Maps and Chaotic Behavior, Chapman & Hall, London, 1992.
    E. Ott, Chaos in Dynamical Systems, Cambridge, 1993.
    V. I. Arnold, Ordinary Differential Equations, MIT Press, 1978.
    V. I. Arnold, Mathematical Methods of Classical Mechanics, Springer, 1989.
    V. I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations, Springer, 1988.

     
    Description:
     
    The CAAM 435 course will provide an overview of Nonlinear Dynamics theory. Our discussions will examine various examples of dynamical systems and provide you with hands-on experience in qualitative and quantitative analytic techniques to better understand dynamical maps and flows; equilibria and stability; integrability and chaotic phenomena; periodic, quasiperiodic and chaotic orbits; Poincaré maps and Smale horseshoes; free, forced and coupled oscillators; the geometry of the dynamics in phase space, bifurcations and catastrophes. We will also discuss applications of dynamical systems theory to physics, neuroscience and biology.
    Grading:
  • 40% exams, 60% problem sets. Students are strongly encouraged to participate in lectures and recitations. Class participation will influence borderline grades and help to improve overall performance.
  • Exams: Two take-home open-book exams, which must be your individual, unassisted effort, will account for 40% of the final grade (20% each).
  • Homework assignments: Problem sets will be assigned roughly once a week, due at 7 pm on the specified date. Analytical solutions for all problems are expected. Your submitted write-up must be your own independent work, but you may collaborate on the problems.
  • Late Policy: You may turn in two problem sets one class period late. Subsequent late assignments will be penalized 15% each. No two `lates' on one assignment, without a written excuse. In exceptional circumstances, please contact the instructor as soon as possible: we adhere to Student Health's `No Note' policy.
    • ?