# Chaotic Systems Toolbox

### Alexandros Leontitsis (view profile)

11 Apr 2002 (Updated )

Analysis of chaotic systems.

[Y,T]=derivs(x,dim)
```function [Y,T]=derivs(x,dim)
%Syntax: [Y,T]=derivs(x,dim)
%____________________________
%
% The phase space reconstruction of a time series x whith the derivatives approach,
% in embedding dimension m.
%
% Y is the trajectory matrix in the reconstructed phase space.
% T is the phase space length.
% x is the time series.
% dim is the embedding dimension.
%
%
% Reference:
%
% Packard N H, Cruchfield J P, Farmer J D, Shaw R S (1980): Geometry from a Time
% Series. Physical Review Letters 45: 712-715
%
%
% Alexandros Leontitsis
% Department of Education
% University of Ioannina
% 45110 - Dourouti
% Ioannina
% Greece
%
% University e-mail: me00743@cc.uoi.gr
% Homepage: http://www.geocities.com/CapeCanaveral/Lab/1421
%
% 11 Mar 2001.

if nargin<1 | isempty(x)==1
error('You should provide a time series.');
else
% x must be a vector
if min(size(x))>1
error('Invalid time series.');
end
x=x(:);
% N is the time series length
N=length(x);
end

if nargin<2 | isempty(dim)==1
dim=2;
else
% dim must be scalar
if sum(size(dim))>2
error('dim must be scalar.');
end
% dim must be an integer
if dim-round(dim)~=0
error('dim must be an integer.');
end
% dim must be positive
if dim<=0
error('dim must be positive.');
end
end

% Initialize the phase space
Y=zeros(N,dim);

% Phase space reconstruction with the derivatives approach
Y(:,1)=x;
for i=2:dim
Y(:,i)=[diff(Y(:,i-1));0];
end

% Total points on phase space
T=N-(dim-1);

% Remove the meaningless points
Y(T+1:end,:)=[];
```