MATLAB Software

Dynamical Systems

  • 2-dimensional Iterated Function Systems (IFS)
    Plots the attractor of a generic 2-dimensional (linear) IFS by chaos game.
    [X,h] = ifs(A, p, N, opt1)
    Some examples of the use of ifs.m are here:

  • Self-organized criticality in a model of production and inventory dynamics
    A raw and simple program to numerically simulate the model developed by:
    P. Bak, K. Chen, J. Scheinkman and M. Woodford (1993),
    Aggregate Fluctuations from Independent Sectoral Shocks: Self-Organized Criticality
    in a Model of Production and Inventory Dynamics
    , Ricerche Economiche, 47 (1), 3-30.
    Click here to download a screenshot of the program.

  • Endogenous preferences and relational dynamics
    The simulation software of the model presented in
    Biavati M., Sandri M., Zarri L. (2002),
    Preferenze endogene e dinamiche relazionali: un modello co-evolutivo,
    in Sacco P.L. e Zamagni S. (a cura di),
    Complessità relazionale e comportamento economico.
    Verso un nuovo paradigma di razionalità, ll Mulino, Bologna

    Plot of High Dimensional Data

  • Andrews Diagrams
    Plots high-dimensional data using the method proposed by Andrews (1972).
    Y = ANDREWS(X,N) plots each row of the matrix X as a trigonometric function defined in the interval (-pi,pi).
    N is the number of points taken into account in the interval(-pi,pi). The default value for N is 100.
    Y is the matrix containing the values f(t) of the trigonometric functions.
    Reference: D.F. Andrews (1972), "Plots of High-Dimensional data", Biometrics, pp. 125-136
    An example of the use of andrews.m is: testandr.m

    Mathematica Packages

    Nonlinear dynamical systems

  • Numerical Calculation of Lyapunov Exponents
    The Lyapunov characteristic exponents play a crucial role in the description of the behavior
    of dynamical systems. They measure the average rate of divergence or convergence of orbits
    starting from nearby initial points. Therefore, they can be used to analyze the stability of limit
    sets and to check sensitive dependence on initial conditions, that is, the presence of chaotic
    This package shows how to use Mathematica to compute the Lyapunov spectrum of a smooth
    dynamical system.
    The lce.m Mathematica package (for Mathematica < 5.2)
    The lce.m Mathematica package (for Mathematica >7)
    A notebook with all the (updated) code used in the paper (for Mathematica 12)

    Time series analysis

  • MELISSA: a Mathematica package for Singular Spectrum Analysis
  • Singular spectrum analysis (SSA) is a relatively recent technique for time series analysis.
    The idea behind SSA was originally purposed as a data adaptive method for choosing an optimal
    embedding dimension for attractor reconstruction. Later the technique was developed as a "stand
    alone" time series analysis technique.
    During the last decade it has been very successful and has become a standard tool in many different
    scientific fields, such as climatic, meteorological, geophysical, and astronomical time series analysis.
    Download the tutorial for MELISSA (in italian)

  • Updated: 12 Oct 2022