Digitally generating true orbits of binary shift chaotic maps and their conjugates

Ozturk I., KILIÇ R.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, cilt.62, ss.395-408, 2018 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 62
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1016/j.cnsns.2018.02.039
  • Dergi Adı: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.395-408
  • Anahtar Kelimeler: Dynamical maps, True chaotic orbits, FPGA, Topological conjugacy, IMAGE ENCRYPTION, LOGISTIC MAP, TENT MAP, ALGORITHM, CRYPTOSYSTEMS, COMPUTATION
  • Erciyes Üniversitesi Adresli: Evet

Özet

It is impossible to obtain chaotic behavior using conventional finite precision calculations on a digital platform. All such realizations are eventually periodic. Also, digital calculations of the periodic orbits are often erroneous due to round-offand truncation errors. Because of these errors, periodic orbits quickly diverge from the true orbit and they end up into one of the few cycles that occur for almost all initial conditions. Hence, digital calculations of chaotic systems do not represent the true orbits of the mathematically defined original system. This discrepancy becomes evident in the simulations of the binary shift chaotic maps like Bernoulli map or tent map. Although these systems are perfectly well defined chaotic systems, their digital realizations always converge to zero. In the literature, there are some studies which replace the least significant zero bits by random bits to overcome this problem.