Hidden Periodicity – Chaos Dependance on Numerical Precision

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 210)


Deterministic chaos has been observed in many systems and seems to be random-like for external observer. Chaos, especially of discrete systems, has been used on numerous occasions in place of random number generators in so called evolutionary algorithms. When compared to random generators, chaotic systems generate values via so called map function that is deterministic and thus, the next value can be calculated, i.e. between elements of random series is no deterministic relation, while in the case of chaotic system it is. Despite this fact, the very often use of chaotic generators improves the performance of evolutionary algorithms. In this paper, we discuss the behavior of two selected chaotic system (logistic map and Lozi system) with dependance on numerical precision and show that numerical precision causes the appearance of many periodic orbits and explain reason why it is happens.


Periodic Orbit Evolutionary Algorithm Chaotic System Deterministic Chaos Numerical Precision 
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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  1. 1.VSB-Technical University of OstravaOstrava-PorubaCzech Republic
  2. 2.Faculty of Applied InformaticsTomas Bata University in ZlinZlinCzech Republic
  3. 3.Laboratory of Modeling, Information & Systems (MIS)University of Picardie Jules Verne (UPJV)Amiens Cedex 1France
  4. 4.Department of Computer ScienceUniversity of VaasaVaasaFinland

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