File Exchange

Lyapunov exponent of logistic map

version 1.1.2 (1.5 KB) by Valentina Unakafova

Valentina Unakafova (view profile)

Computes estimated values of Lyapunov exponent of logistic map for r within the interval (3.5,4)

Updated 07 Sep 2018

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

ervin

Matlab

Matlab (view profile)

Thanks

Valentina Unakafova

Valentina Unakafova (view profile)

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

Matlab (view profile)

Is LE value represent the initial value of map?