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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


A Numerical Analysis of Poincar'{e} Chaos

Discontinuity, Nonlinearity, and Complexity 12(1) (2023) 183--195 | DOI:10.5890/DNC.2023.03.013

Marat Akhmet$^1$, Mehmet Onur Fen$^{2}$, Astrit Tola$^1$

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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, Poincar\'{e} 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 R\"{o}ssler 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.


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