Effect of randomness in logistic maps

Abdul Khaleque and Parongama Sen
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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

International Journal of Modern Physics C (IJMPC), 2015, vol. 26, issue 08, 1-11

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.

Keywords: Ergodicity; chaos; Lyapunov exponent; threshold behaviour; nature-versus-nurture; 05.45.-a; 05.90.+m; 87.23; 74.40.De (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1142/S0129183115500862

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