Title: SYMBOLIC DYNAMICS AND SPIRAL STRUCTURES DUE TO THE SADDLE-FOCUS BIFURCATIONS
Abstract: Chaos, CNN, Memristors and Beyond, pp. 428-439 (2013) No AccessSYMBOLIC DYNAMICS AND SPIRAL STRUCTURES DUE TO THE SADDLE-FOCUS BIFURCATIONSANDREY SHILNIKOV, LEONID SHILNIKOV, and ROBERTO BARRIOANDREY SHILNIKOVNeuroscience Institute and Department of Mathematics and Statistics, Georgia State University, Atlanta 30303, USA, LEONID SHILNIKOVInstitute for Applied Mathematics and Cybernetics, Nizhniy Novgorod, 603006 Russia, Russia(17/12/1934–26/12/2011), and ROBERTO BARRIODepartamento de Matemática Aplicada and IUMA, University of Zaragoza, E-50009. Spain, Spainhttps://doi.org/10.1142/9789814434805_0033Cited by:3 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Abstract: We examine spiral structures in bi-parametric diagrams of dissipative systems with strange attractors. We show that the organizing center for spiral structures in the Rössler model with the saddle-focus equilibria is related to the change of the structure of the attractor transitioning between the spiral and screw-like types. The structure skeleton is formed by saddlenode bifurcation curves originating from a codimension-two Belyakov point corresponding to the transition to the saddle-focus from a simple saddle. A new computational technique based on the symbolic kneading invariant description for examining dynamical chaos and parametric chaos in systems with Lorenz-like attractors is proposed and tested. This technique uncovers the stunning complexity and universality of spiral structures in the iconic Lorenz equations. FiguresReferencesRelatedDetailsCited By 3On the topology of the Lorenz systemTali Pinsky20 September 2017 | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 473, No. 2205Symbolic Toolkit for Chaos ExplorationsTingli Xing, Jeremy Wojcik, Roberto Barrio and Andrey Shilnikov14 December 2013Discontinuous Spirals of Stable Periodic OscillationsAchim Sack, Joana G. Freire, Erik Lindberg, Thorsten Pöschel and Jason A. C. Gallas27 November 2013 | Scientific Reports, Vol. 3, No. 1 Chaos, CNN, Memristors and BeyondMetrics History PDF download
Publication Year: 2013
Publication Date: 2013-02-06
Language: en
Type: book-chapter
Indexed In: ['crossref']
Access and Citation
Cited By Count: 5
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