System approach of solving direct and reverse tasks in systems with chaos

Authors

  • Valery Ya. Danylov Institute for Applied System Analysis of National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine https://orcid.org/0000-0003-3389-3661
  • Artem Yu. Zinchenko The Department of Software Systems and Technologies of Taras Shevchenko National University of Kyiv, Kyiv, Ukraine https://orcid.org/0000-0003-1586-3645
  • V. Ya. Danilov The Department of General Mathematics of Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

DOI:

https://doi.org/10.20535/SRIT.2308-8893.2017.2.01

Keywords:

deterministic chaos, YU.-SH. Chen nonlinear system, bifurcation, reconstruction of mathematical model

Abstract

In this paper, the systematic approach to the effective application of mathematical and computer modeling of dynamic systems is proposed for solving the problems of deterministic chaos research in complex nonlinear systems and related inverse problems. The scientific and technical task of enhancing mathematical modeling by improving existing methodologies of investigation of the deterministic chaos and by developing new mathematical models, based on the specialization of existing ones, is solved. To solve the problem, we suggested investigation schemes of direct (research modes of behavior depending on the bifurcation parameters) and inverse (reconstruction of mathematical models) tasks of the deterministic chaos in complex non-linear systems. Experimental studies are presented for scalar implementations of YU.-SH. Chen and Roessler nonlinear systems. For the last one, the equivalent model was constructed.

Author Biographies

Valery Ya. Danylov, Institute for Applied System Analysis of National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv

Danilov Valery,

Doctor of Engineering Sciences, professor at the Institute for Applied System Analysis of National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute".

Graduated from the Taras Shevchenko Kyiv National University in 1972, department of cybernetics.

He got his PhD (Candidate of Physical and Mathematical Sciences) degree in Control Engineering in 1979, and Doctor of Engineering Sci. in 1993.

Current areas of interest: system analysis, identification and control of dynamic systems with chaos, fractal analysis, and artificial intelligence.

Artem Yu. Zinchenko, The Department of Software Systems and Technologies of Taras Shevchenko National University of Kyiv, Kyiv

Artem Zinchenko,

candidate of technical sciences, a teaching assistant at the Department of Software Systems and Technologies of Taras Shevchenko National University of Kyiv, Kyiv, Ukraine.

V. Ya. Danilov, The Department of General Mathematics of Taras Shevchenko National University of Kyiv, Kyiv

Volodymyr Danilov,

associate professor, canditate of phys.-math. sciences, associate professor at the Department of General Mathematics of Taras Shevchenko National University of Kyiv, Kyiv, Ukraine.

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Published

2017-06-26

Issue

No. 2 (2017)

Section

Theoretical and applied problems and methods of system analysis

License

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