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Study of dynamical systems from the viewpoint of complexity and computational capabilities

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Abstract

We study a system of nonlinear differential equations that can sort numbers fed to the input as the initial conditions. We suggest a method that permits using similar systems to solve conditional optimization problems. We show that the trace maximization property ensuring the solution of the sorting problem holds for a more general class of systems. A number of modifications and generalizations are suggested.

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References

  1. Bournez, O. and Campagnolo, M.L., A Survey on Continuous Time Computations, in New Computational Paradigms, New York, 2008, pp. 383–423.

    Chapter  Google Scholar 

  2. Chu, M.T., Linear Algebra Algorithms as Dynamical Systems, Acta Numerica, 2008, vol. 17, pp. 1–86.

    Article  MathSciNet  MATH  Google Scholar 

  3. Brockett, R.W., Dynamical Systems That Sort Lists, Diagonalize Matrices and Solve Linear Programming Problems, Decision and Control: Proceedings of the 27th IEEE Conference on IEEE, 1988, pp. 799–803.

    Chapter  Google Scholar 

  4. Bloch, A.M., Steepest Descent, Linear Programming and Hamiltonian Flows, Contemp. Math. AMS, 1990, vol. 114, pp. 77–88.

    Article  MathSciNet  MATH  Google Scholar 

  5. Bennett, C.H., Logical Reversibility of Computation, Maxwellś Demon. Entropy, Information, Computing, 1973, pp. 197–204.

    Google Scholar 

  6. Bogoyavlenskii, O.I., Oprokidyvayushchiesya solitony, nelineinye integriruemye uravneniya (Overturning Solitons. Nonlinear Integrable Equations), Moscow: Nauka, 1991.

    Google Scholar 

  7. Prasolov, V.V., Zadachi i teoremy lineinoi algebry (Problems and Theorems of Linear Algebra), Moscow, 1996.

    Google Scholar 

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology, Moscow, Russia

    A. A. Gladkikh & G. G. Malinetskii

  2. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia

    A. A. Gladkikh & G. G. Malinetskii

Authors
  1. A. A. Gladkikh
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  2. G. G. Malinetskii
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Corresponding author

Correspondence to A. A. Gladkikh.

Additional information

Original Russian Text © A.A. Gladkikh, G.G. Malinetskii, 2016, published in Differentsial’nye Uravneniya, 2016, Vol. 52, No. 7, pp. 937–945.

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Gladkikh, A.A., Malinetskii, G.G. Study of dynamical systems from the viewpoint of complexity and computational capabilities. Diff Equat 52, 897–905 (2016). https://doi.org/10.1134/S0012266116070090

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  • DOI: https://doi.org/10.1134/S0012266116070090

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