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: ifs.zip
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
Plots high-dimensional data using the method proposed by Andrews
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.
the matrix containing the values f(t) of the trigonometric
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
Nonlinear dynamical systems
Numerical Calculation of Lyapunov Exponents
The Lyapunov characteristic exponents play a crucial role in the description of the
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
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