chapter12_deterministic.md

12. Deterministic Dynamical Systems

Full list of references in Chapter 12 of the IPython Cookbook, the definitive guide to high-performance scientific computing and data science in Python, by Dr. Cyrille Rossant, Packt Publishing, 400 pages, 2014.

Recipe 1

• Chaos theory.
• Complex systems are particular chaotic systems.
• The logistic map.
• Iterated functions (discrete dynamical systems).
• Bifurcation diagrams.
• Lyapunov exponent.

Recipe 2

• Cellular automata.
• Elementary cellular automata.
• Rule 110, a Turing-complete automaton.
• The Wolfram code assigns a 1D elementary cellular automaton to any number between 0 and 255.

Recipe 3

Recipe 4

• Partial Differential Equations,
• Reaction-diffusion systems,
• Fitzhugh-Nagumo system,
• Neumann boundary conditions,
• Von Neumann stability analysis.