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Rus. J. Nonlin. Dyn., 2021, Volume 17, Number 2, Pages 157–164 (Mi nd747)  

Mathematical problems of nonlinearity

On the Organization of Homoclinic Bifurcation Curves in Systems with Shilnikov Spiral Attractors

Y. V. Bakhanova, A. A. Bobrovsky, T. K. Burdygina, S. M. Malykh

National Research University “Higher School of Economics”, ul. Bolshaya Pecherskaya 25/12, Nizhny Novgorod, 603155 Russia

Abstract: We study spiral chaos in the classical Rössler and Arneodo –Coullet –Tresser systems. Special attention is paid to the analysis of bifurcation curves that correspond to the appearance of Shilnikov homoclinic loop of saddle-focus equilibrium states and, as a result, spiral chaos. To visualize the results, we use numerical methods for constructing charts of the maximal Lyapunov exponent and bifurcation diagrams obtained using the MatCont package.

Keywords: Shilnikov bifurcation, spiral chaos, Lyapunov analysis

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 075-15-2019-1931
Russian Science Foundation 19-71-10048
This paper was supported by the Laboratory of Dynamical Systems and Applications NRU HSE, of the Ministry of Science and Higher Education of the RF grant No. 075-15-2019-1931. Numerical results presented in Section 2 were obtained by the RSF grant 19-71-10048.


DOI: https://doi.org/10.20537/nd210202

Full text: PDF file (5045 kB)
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MSC: 37G10, 37G35
Received: 20.05.2021
Accepted:09.06.2021
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Citation: Y. V. Bakhanova, A. A. Bobrovsky, T. K. Burdygina, S. M. Malykh, “On the Organization of Homoclinic Bifurcation Curves in Systems with Shilnikov Spiral Attractors”, Rus. J. Nonlin. Dyn., 17:2 (2021), 157–164

Citation in format AMSBIB
\Bibitem{BakBobBur21}
\by Y. V. Bakhanova, A. A. Bobrovsky, T. K. Burdygina, S. M. Malykh
\paper On the Organization of Homoclinic Bifurcation Curves in Systems with Shilnikov Spiral Attractors
\jour Rus. J. Nonlin. Dyn.
\yr 2021
\vol 17
\issue 2
\pages 157--164
\mathnet{http://mi.mathnet.ru/nd747}
\crossref{https://doi.org/10.20537/nd210202}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85109460326}


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