Compartmental Unpredictable Functions

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AKHMET M., Tleubergenova M., Zhamanshin A.

Mathematics, vol.11, no.5, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 5
  • Publication Date: 2023
  • Doi Number: 10.3390/math11051069
  • Journal Name: Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: unpredictable functions, compartmental unpredictable functions, degree of periodicity, functions determined deterministically and randomly, numerical simulations, POINCARE CHAOS, SYNCHRONIZATION
  • Middle East Technical University Affiliated: Yes


There is a huge family of recurrent functions, which starts with equilibria and ends with Poisson stable functions. They are fundamental in theoretical and application senses, and they admit a famous history. Recently, we have added the unpredictable functions to the family. The research has been performed in several papers and books. Obviously, theoretical and application merits of functions increase if one provides rigorously approved efficient methods of construction of concrete examples, as well as their numerical simulations. In the present study, we met the challenges for unpredictability by considering functions of two variables on diagonals. Algorithms have been created, and they are both deterministic and random. Characteristics are introduced to evaluate contributions of periodic and unpredictable components to the dynamics, and they are clearly illustrated in graphs of the functions. Definitions of non-periodic compartmental functions are provided as suggestions for the research in the future.