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A new hybrid nonlinear congruential number generator based on higher functional power of logistic maps

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  • Cecen, Songul
  • Demirer, R. Murat
  • Bayrak, Coskun

Abstract

We propose a nonlinear congruential pseudorandom number generator consisting of summation of higher order composition of random logistic maps under certain congruential mappings. We change both bifurcation parameters of logistic maps in the interval of U=[3.5599,4) and coefficients of the polynomials in each higher order composition of terms up to degree d. This helped us to obtain a perfect random decorrelated generator which is infinite and aperiodic. It is observed from the simulation results that our new PRNG has good uniformity and power spectrum properties with very flat white noise characteristics. The results are interesting, new and may have applications in cryptography and in Monte Carlo simulations.

Suggested Citation

  • Cecen, Songul & Demirer, R. Murat & Bayrak, Coskun, 2009. "A new hybrid nonlinear congruential number generator based on higher functional power of logistic maps," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 847-853.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:2:p:847-853
    DOI: 10.1016/j.chaos.2009.02.014
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    References listed on IDEAS

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    1. Iovane, Gerardo, 2009. "The set of primes: Towards an optimized algorithm, prime generation and validation, and asymptotic consequences," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1344-1352.
    2. Iovane, Gerardo, 2008. "The distribution of prime numbers: The solution comes from dynamical processes and genetic algorithms," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 23-42.
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