A Numerical Analysis of Poincare Chaos

AKHMET M., Fen M. O., Tola A.

Discontinuity, Nonlinearity, and Complexity, vol.12, no.1, pp.183-195, 2023 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 1
  • Publication Date: 2023
  • Doi Number: 10.5890/dnc.2023.03.013
  • Journal Name: Discontinuity, Nonlinearity, and Complexity
  • Journal Indexes: Scopus
  • Page Numbers: pp.183-195
  • Keywords: Lorenz system, Poincaré chaos, Rössler system, Sequential test, Unpredictable solutions
  • TED University Affiliated: Yes


This paper reveals a new way to indicate the presence of chaos in continuous-time models, beside other techniques such as the method of Lyapunov exponents and bifurcation diagrams. The sequential test confirms the existence of an unpredictable solution, and therefore, Poincaré chaos for differential equations. The main part of the study consists of the description of the novel algorithm, demonstrating its convenience for analysis of chaotic dynamics. The procedure facilities are carefully determined, and they are implemented to Lorenz and Rössler systems. The peculiarity of the method lies in the fact that in addition to the indication of just chaos, we clarify the divergence character of a single trajectory, which is based on the unpredictability feature. Potentially it can be more effective than the conventional ways for indication of chaos. The presence of chaos is also approved in the case of zero largest Lyapunov exponent