Bibliography | Avrutin, Viktor; Schanz, Michael; Gardini, Laura: Calculation of Bifurcation Curves by Map Replacement. In: International Journal of Bifurcation and Chaos. Vol. 20(10). University of Stuttgart, Faculty of Computer Science, Electrical Engineering, and Information Technology. pp. 3105-3135, english. World Scientific Publishing Company, December 2010. DOI: 10.1142/S0218127410027581. Article in Journal.
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CR-Schema | J.2 (Physical Sciences and Engineering)
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Keywords | Discontinuous piecewise-linear 1D map; border collision bifurcation curves; map replacement technique; rested period adding; Farey structure. |
Abstract | The complex bifurcation structure in the parameter space of the general piecewise-linear scalar map with a single discontinuity - nowadays known as nested period adding structure - was completely studied analytically by N. N. Leonov already 50 years ago. He used an elegant and very efficient recursive technique, which allows the analytical calculation of the border-collision bifurcation curves, causing the nested period adding structure to occur. In this work, we have demonstrated that the application of Leonov's technique is not resticted to that particular bifurcation structure. On the contrary, the presented map replacement approach, which is an extension of Leonov's technique, allows the analytical calculation of border-collision bifurcation curves for periodic orbits with high periods and complex symbolic sequences using appropriate composite maps and the bifurcation curves for periodic orbits with much lower periods.
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Copyright | World Scientific Publishing Company |
Contact | Viktor.Avrutin@ipvs.uni-stuttgart.de |
Department(s) | University of Stuttgart, Institute of Parallel and Distributed Systems, Image Understanding
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Project(s) | Organisationszentren in nichtglatten dynamischen Systemen: Bifurkationen höherer Kodimension in Theorie und Anwendungen AnT 4.669
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Entry date | January 24, 2011 |
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