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Effect of randomness in logistic maps

Author

Listed:
  • Abdul Khaleque

    (Department of Physics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700009, India)

  • Parongama Sen

    (Department of Physics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700009, India)

Abstract

We study a random logistic mapxt+1= atxt[1 - xt]whereatare bounded(q1≤ at≤ q2), random variables independently drawn from a distribution.xtdoes not show any regular behavior in time. We find thatxtshows fully ergodic behavior when the maximum allowed value ofatis 4. However〈xt→∞〉, averaged over different realizations reaches a fixed point. For1 ≤ at≤ 4, the system shows nonchaotic behavior and the Lyapunov exponent is strongly dependent on the asymmetry of the distribution from whichatis drawn. Chaotic behavior is seen to occur beyond a threshold value ofq1(q2)whenq2(q1)is varied. The most striking result is that the random map is chaotic even whenq2is less than the threshold value 3.5699⋯ at which chaos occurs in the nonrandom map. We also employ a different method in which a different set of random variables are used for the evolution of two initially identicalxvalues, here the chaotic regime exists for allq1≠ q2values.

Suggested Citation

  • Abdul Khaleque & Parongama Sen, 2015. "Effect of randomness in logistic maps," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 26(08), pages 1-11.
    • Handle: RePEc:wsi:ijmpcx:v:26:y:2015:i:08:n:s0129183115500862
    DOI: 10.1142/S0129183115500862
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