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## Lyapunov exponent of logistic map

version 1.1.2 (1.5 KB) by
Computes estimated values of Lyapunov exponent of logistic map for r within the interval (3.5,4)

Updated 07 Sep 2018

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function LE = LEofLogisticMap( rStart, rEnd, rStep )
calculates Lyapunov exponent of logistic map x(t+1) = r*x(t)*(1-x(t)) for r within the interval (3.5,4) using derivative for values of control parameter from rStart to rEnd with step rStep

INPUT
- rStart - first value of control parameter r
- rEnd - last value of control parameter r
- rStep - step

OUTPUT
- LE - values of estimated Lyapunov exponent according to [S03]

EXAMPLE OF USE:
rStart = 3.5;
rEnd = 4;
rStep = 0.0001;
LE = LEofLogisticMap( rStart, rEnd, rStep );
figure; plot( rStart:rStep:rEnd, LE, 'k.-' ); axis tight;
title('Values of estimated Lyapunov exponent for logistic map for r = 3.5...4' );
xlabel( 'r' );
ylabel( 'Values of estimated Lyapunov exponent' );

REFERENCES
[S03] J.C. Sprott, 2003. Chaos and time-series analysis, volume 69. Oxford University Press Oxford.
%
% @author Valentina Unakafova
% @email UnakafovaValentina(at)gmail.com
% @date 11.07.2017

### Cite As

Valentina Unakafova (2020). Lyapunov exponent of logistic map (https://www.mathworks.com/matlabcentral/fileexchange/63803-lyapunov-exponent-of-logistic-map), MATLAB Central File Exchange. Retrieved .

ervin

Matlab

Thanks

Valentina Unakafova

Hello Matlab,
LE values represent the estimated values of Lyapunov exponent computed for the logistic map for the parameters r from 3.5 to 4. The values are estimated by the formula from J.C. Sprott, 2003 (Chaos and time-series analysis, volume 69. Oxford University Press Oxford.)

Matlab

Is LE value represent the initial value of map?

##### MATLAB Release Compatibility
Created with R2013b
Compatible with any release
##### Platform Compatibility
Windows macOS Linux