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TMF, 2002, Volume 130, Number 2, Pages 287–300 (Mi tmf303)  

This article is cited in 2 scientific papers (total in 2 papers)

Dissipative and Hamiltonian Systems with Chaotic Behavior: An Analytic Approach

A. K. Abramyan, S. A. Vakulenko

Institute of Problems of Mechanical Engineering, Russian Academy of Sciences

Abstract: Some classes of dissipative and Hamiltonian distributed systems are described. The dynamics of these systems is effectively reduced to finite-dimensional dynamics which can be unboundedly complex in a sense. Yarying the parameters of these systems, we can obtain an arbitrary (to within the orbital topological equivalence) structurally stable attractor in the dissipative case and an arbitrary polynomial weakly integrable Hamiltonian in the conservative case. As examples, we consider Hopfield neural networks and some reaction-diffusion systems in the dissipative case and a nonlinear string in the Hamiltonian case.

DOI: https://doi.org/10.4213/tmf303

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English version:
Theoretical and Mathematical Physics, 2002, 130:2, 245–255

Bibliographic databases:

Received: 24.05.2001

Citation: A. K. Abramyan, S. A. Vakulenko, “Dissipative and Hamiltonian Systems with Chaotic Behavior: An Analytic Approach”, TMF, 130:2 (2002), 287–300; Theoret. and Math. Phys., 130:2 (2002), 245–255

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Danca M.-F., Kuznetsov N., “Hidden Chaotic Sets in a Hopfield Neural System”, Chaos Solitons Fractals, 103 (2017), 144–150  crossref  mathscinet  zmath  isi  scopus  scopus
    2. Vaseghi B., Pourmina M.A., Mobayen S., “Finite-Time Chaos Synchronization and Its Application in Wireless Sensor Networks”, Trans. Inst. Meas. Control, 40:13 (2018), 3788–3799  crossref  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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