Teaching :: Nonlinear Dynamical Systems (AM 114/214)

Additional Course Material

Bifurcation theory 

  1. Elements of applied bifurcation theory for n-dimensional dynamical systems (PDF)

Numerical Methods

  1. How to use Mathematica to compute Lyapunov spectrum of a smooth dynamical system (PDF)
  2. Numerical bifurcation methods and their application to fluid dynamics (PDF)
  3. Computing Lyapunov exponents from time series (PDF) (Matlab code)
  4. Computing Poicaré maps (PDF)
  5. Matlab software for bifurcation analysis in continuous and discrete dynamical systems (MatCont - documentation PDF)

Papers on Nonlinear Dynamics

  1. E. J. Doedel, B. Krauskopf and H. M. Osinga,``Global bifurcations of the Lorenz manifold'', Nonlinearity 19 (2006), 2297 (PDF)

Foundational Papers on Nonlinear Dynamics and Chaos

  1. E. Lorenz, ``Deterministic Nonperiodic Flows'', Journal of the Atmosferic Sciences, 20 (1963), pp. 130-141. (PDF)
  2. D. Ruelle and F. Takens, ``On the Nature of Turbulence'', Comm. Math. Phys., 20 (1971), pp. 167-192. (PDF)
  3. R. M. May, ``Simple Mathematical Models with Very Complicated Dynamics'', Nature., 261 (1976), pp. 459-467. (PDF)
  4. M. Henon, ``A Two-Dimensional Mapping with a Strange Attractor'', Comm. Math. Phys., 50 (1976), pp. 69-77. (PDF)
  5. M. J. Feigenbaum, ``The Transition to Aperiodic Behavior in Turbulent Systems'', Comm. Math. Phys., 77 (1980), pp. 65-86. (PDF)
  6. B. Mandelbrot, ``How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension'', Science., 156 (1967), pp. 636-638. (PDF)
  7. O. E. Rossler, ``An equation for continuous chaos'', Phys. Lett., 57A (1976), pp. 397-398. (PDF)