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Application of Mel’nikov’s method for estimating the efficacy of external signals on complex nonlinear systems with strange attractors

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Abstract

Mel’nikov’s method is used as a criterion for determining the condition for the onset of stochastization in nonlinear dynamical systems with strange attractors. Analytical conditions for the onset of stochastization in Duffing systems and Lorenz systems are obtained, from which one can synthesize a control signal ensuring the required behavior of the system. A mathematical experiment is carried out which confirms the correctness of the theoretical analysis.

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References

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Authors and Affiliations

  1. Kazan State Technical University, Kazan

    V. V. Afanas’ev, Yu. E. Pol’skii & V. S. Chernyavskii

Authors
  1. V. V. Afanas’ev
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  2. Yu. E. Pol’skii
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  3. V. S. Chernyavskii
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Pis’ma Zh. Tekh. Fiz. 23, 40–45 (December 12, 1997)

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Afanas’ev, V.V., Pol’skii, Y.E. & Chernyavskii, V.S. Application of Mel’nikov’s method for estimating the efficacy of external signals on complex nonlinear systems with strange attractors. Tech. Phys. Lett. 23, 917–919 (1997). https://doi.org/10.1134/1.1261932

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  • DOI: https://doi.org/10.1134/1.1261932

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