The content of this page my change over time, depending on how much time I can dedicate to build it.

A complex system is a system composed of interconnected parts that as a whole exhibit one or more properties (behavior among the possible properties) not obvious from the properties of the individual parts.
In the last years, my investigation of complex systems can be summarized by the following (non-exhaustive, unordered, incomplete, nonlinear) random walking in the corresponding complex network of knodges:

Complex systems theory

• Information theory
  • Shannon entropy
  • Renyi entropy
  • Algorithmic information theory
• Nonlinear dynamics
• Statistical physics
  • Entropy
  • Superstatistics
  • Extreme value theory
• Complexity
• Complex adaptive system
• Self-organizing system
• System theory
• Non-equilibrium thermodynamics and Dynamical systems
  • Dissipative system
  • Nonlinear dynamics
    • Chaos theory
    • Time series
    • Ito diffusion
    • Anomalous diffusion
  • Turbulence
• Network science
• Pattern formation
  • Percolation
  • Diffusion-limited aggregation
  • Fractal

But if you want a more complicated idea in a more simplified shape, you can take a look at this figure.

Complex Networks

A very nice application of network theory to real-world can be found in this 1st TED talk and in this 2nd TED talk given by Nicholas Christakis.

Or you can take a look at the following video about the "Controllability of Complex Networks" (see the Barabasi Lab page dedicated to this project), which of course will capture your attention on complex networks:

Nonlinear Dynamics and Time Series Analysis 

1. Free Time Series - Free time series for linear and nonlinear time series analysis generated with TSUT
2. Dynamical Models wiki - Examples of dynamical model simulated with RooTiSA.
3. Complexity Animation - Nonlinearity and Complexity animations from BOC
4. Software - Recommended software for Nonlinear Dynamics Analysis
5. Links - Recommended links

Complexity Animations

• Diffusion Limited Aggregation [View]
• Sea Things [View]
• Lorenz Attractor [View]
• Fractal Invader [View]
• Simple Binary Network [View]
• Binary Network Sound Machine [View]
• Wolfram 8-bit 1D Cellular Automata [View]
• One Legged Creatures [View]
• Spring / Mass / Motor system [View]

Software

 

• ROOT [Homepage] [Doc]
• TISEAN [Homepage] [Doc]   [Mac OS X 10.5 Binaries]
• R [Homepage] [Doc]
• IT++ [Homepage] [Doc]

Netlib (a collection of mathematical software, papers, and databases) [Homepage]:

• BLAS (Basic Linear Algebra Subprograms) [Homepage]
• LAPACK (Linear Algebra PACKage) [Homepage]
• ARMADILLO (C++ linear algebra library) [Homepage]

Libraries:

• FFTW (Fastest Fourier Transform in the West) [Homepage]
• ATLAS (Automatically Tuned Linear Algebra Software) [Homepage]
• IMKL (Intel Math Kernel Library) [Homepage]
• ACML (AMD Core Math Library) [Homepage]
• CEPHES (Mathematical Library) [Homepage]

Klick to see chaos Funny video!

Links

• Recurrence Plots
• Numerical Recipes
• Scientific Computing Software
• Linux Software Encyclopedia
• Free software for physicists
• Chaos on the web
• Statistics glossary
• Chaos journal
• Nonlinearity and Chaos links
• Breath of Complexity

 

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