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Lyapunov exponent of logistic map

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

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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

Comments and Ratings (4)

ervin

Matlab

Thanks

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?

Updates

1.1.2

Cover picture has been changed

1.1.1.0

Description is renewed

1.1.0.0

Example of use and cover picture are added

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