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Russian Journal of Nonlinear Dynamics, 2022, Volume 18, Number 2, Pages 171–181
DOI: https://doi.org/10.20537/nd220202
(Mi nd785)
 

This article is cited in 3 scientific papers (total in 3 papers)

Nonlinear physics and mechanics

A Method of Investigating the Phenomenon of Bifurcation Memory in the Dynamics of River Vessels

A. V. Chernyshova, S. A. Chernyshovab

a Nizhny Novgorod State Technical University named after R.E. Alekseev, ul. Minina 24, Nizhny Novgorod, 603950, Russia
b HSE University, ul. Bolshaya Pecherskaya 25/12, Nizhny Novgorod, 603155, Russia
References:
Abstract: The phenomenon of “bifurcation memory”, which can be detected during the steering of river vessels, is considered by researchers with the questions of equilibrium point’s bifurcations. It was noticed that in some dynamic systems during saddle-node bifurcation, areas are formed on the phase plane (so-called “phase spot”), passing through which the phase velocity of the representative point decreases. A decrease in phase velocity (e. g. during the steering of river vessel) can cause navigation accidents during shallow waters navigation. In order to improve sailing safety, it is necessary to investigate topological features of phase spots under any possible environmental conditions and steering angle values. In this paper, we propose a new method that makes it easy to get information about the localization of regions with decreased phase velocity. We gained the results related to the topology of areas of different types of motion (accelerated or decelerated) of representative point. In addition, the paper presents the process of evolution of these regions, according to the change of steering angles, as well as before and after the bifurcation. The new method, offered in the article, is more accurate for determining the boundaries of the areas compared to the methods of Feigin and Chirkova. This will allow us to make more correct predictions of changes in the dynamics of the object. The practical implication of the suggested method is that by using it, we can get information about the location of areas with different types of motion of the representative point on the phase plane for different values of steering angle and environmental conditions. This information can be used in the control algorithm of the driving object, for example, in order to predict the decreasing of phase velocities.
Keywords: bifurcation memory, bifurcations in dynamic systems, steering of vessels, Static- Dynamic plane, phase spots.
Received: 30.01.2022
Accepted: 03.05.2022
Bibliographic databases:
Document Type: Article
MSC: 70K05
Language: english
Citation: A. V. Chernyshov, S. A. Chernyshova, “A Method of Investigating the Phenomenon of Bifurcation Memory in the Dynamics of River Vessels”, Rus. J. Nonlin. Dyn., 18:2 (2022), 171–181
Citation in format AMSBIB
\Bibitem{CheChe22}
\by A. V. Chernyshov, S. A. Chernyshova
\paper A Method of Investigating the Phenomenon of
Bifurcation Memory in the Dynamics of River Vessels
\jour Rus. J. Nonlin. Dyn.
\yr 2022
\vol 18
\issue 2
\pages 171--181
\mathnet{http://mi.mathnet.ru/nd785}
\crossref{https://doi.org/10.20537/nd220202}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4445314}
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  • https://www.mathnet.ru/eng/nd/v18/i2/p171
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Russian Journal of Nonlinear Dynamics
     
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