Puy, Andreu; Daza, Alvar; Wagemakers, Alexandre; Sanjuán, Miguel A. F. A test for fractal boundaries based on the basin entropy. (English) Zbl 07299003 Commun. Nonlinear Sci. Numer. Simul. 95, Article ID 105588, 9 p. (2021). MSC: 37C45 37A35 37C75 37D45 PDF BibTeX XML Cite \textit{A. Puy} et al., Commun. Nonlinear Sci. Numer. Simul. 95, Article ID 105588, 9 p. (2021; Zbl 07299003) Full Text: DOI
Christian, J. M.; Middleton-Spencer, H. A. J. On the \(n\)th roots of \(-1\) and complex basin boundaries: fractals from Newton-Raphson. (English) Zbl 1445.97022 Coll. Math. J. 51, No. 2, 95-104 (2020). MSC: 97I99 28A80 PDF BibTeX XML Cite \textit{J. M. Christian} and \textit{H. A. J. Middleton-Spencer}, Coll. Math. J. 51, No. 2, 95--104 (2020; Zbl 1445.97022) Full Text: DOI
Lazarek, M.; Brzeski, P.; Solecki, W.; Perlikowski, P. Detection and classification of solutions for systems interacting by soft impacts with sample-based method. (English) Zbl 1446.34060 Int. J. Bifurcation Chaos Appl. Sci. Eng. 30, No. 6, Article ID 2050079, 11 p. (2020). MSC: 34C15 70K40 34C25 34D20 34A36 PDF BibTeX XML Cite \textit{M. Lazarek} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 30, No. 6, Article ID 2050079, 11 p. (2020; Zbl 1446.34060) Full Text: DOI
Kong, Guiqin; Zhang, Yongxiang Basin reversal in nonlinear driven oscillators. (English) Zbl 1437.34044 Nonlinear Dyn. 96, No. 2, 1213-1231 (2019). MSC: 34C15 34C23 70K55 PDF BibTeX XML Cite \textit{G. Kong} and \textit{Y. Zhang}, Nonlinear Dyn. 96, No. 2, 1213--1231 (2019; Zbl 1437.34044) Full Text: DOI
Li, Zigang; Jiang, Jun; Hong, Ling; Sun, Jian-Qiao On the data-driven generalized cell mapping method. (English) Zbl 1429.37050 Int. J. Bifurcation Chaos Appl. Sci. Eng. 29, No. 14, Article ID 1950204, 21 p. (2019). MSC: 37M99 37C50 PDF BibTeX XML Cite \textit{Z. Li} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 29, No. 14, Article ID 1950204, 21 p. (2019; Zbl 1429.37050) Full Text: DOI
Liu, Xiao-Ming; Jiang, Jun; Hong, Ling; Tang, Dafeng Wada boundary bifurcations induced by boundary saddle-saddle collision. (English) Zbl 1428.37049 Phys. Lett., A 383, No. 2-3, 170-175 (2019). MSC: 37G20 PDF BibTeX XML Cite \textit{X.-M. Liu} et al., Phys. Lett., A 383, No. 2--3, 170--175 (2019; Zbl 1428.37049) Full Text: DOI
Sun, Yong; Ma, Jinpeng; Kurths, Jürgen; Zhan, Meng Equal-area criterion in power systems revisited. (English) Zbl 1402.94134 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 474, No. 2210, Article ID 20170733, 20 p. (2018). MSC: 94C30 37N35 PDF BibTeX XML Cite \textit{Y. Sun} et al., Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 474, No. 2210, Article ID 20170733, 20 p. (2018; Zbl 1402.94134) Full Text: DOI
Hansen, Matheus; da Costa, Diogo Ricardo; Caldas, Iberê L.; Leonel, Edson D. Statistical properties for an open oval billiard: an investigation of the escaping basins. (English) Zbl 1392.37036 Chaos Solitons Fractals 106, 355-362 (2018). MSC: 37D50 37M05 PDF BibTeX XML Cite \textit{M. Hansen} et al., Chaos Solitons Fractals 106, 355--362 (2018; Zbl 1392.37036) Full Text: DOI
Daza, Alvar; Wagemakers, Alexandre; Georgeot, Bertrand; Guéry-Odelin, David; Sanjuán, Miguel A. F. Basin entropy, a measure of final state unpredictability and its application to the chaotic scattering of cold atoms. (English) Zbl 1386.37080 Edelman, Mark (ed.) et al., Chaotic, fractional, and complex dynamics: new insights and perspectives. Cham: Springer (ISBN 978-3-319-68108-5/hbk; 978-3-319-68109-2/ebook). Springer: Complexity; Understanding Complex Systems, 9-34 (2018). MSC: 37N15 34C28 74H65 PDF BibTeX XML Cite \textit{A. Daza} et al., in: Chaotic, fractional, and complex dynamics: new insights and perspectives. Cham: Springer. 9--34 (2018; Zbl 1386.37080) Full Text: DOI
Gyebrószki, Gergely; Csernák, Gábor Clustered simple cell mapping: an extension to the simple cell mapping method. (English) Zbl 07257115 Commun. Nonlinear Sci. Numer. Simul. 42, 607-622 (2017). MSC: 68 92 PDF BibTeX XML Cite \textit{G. Gyebrószki} and \textit{G. Csernák}, Commun. Nonlinear Sci. Numer. Simul. 42, 607--622 (2017; Zbl 07257115) Full Text: DOI
Zhang, Yongxiang Strange nonchaotic attractors with Wada basins. (English) Zbl 1356.37055 Physica D 259, 26-36 (2013). MSC: 37D45 37C70 PDF BibTeX XML Cite \textit{Y. Zhang}, Physica D 259, 26--36 (2013; Zbl 1356.37055) Full Text: DOI
Viana, R. L.; Da Silva, E. C.; Kroetz, T.; Caldas, I. L.; Roberto, M.; Sanjuán, M. A. F. Fractal structures in nonlinear plasma physics. (English) Zbl 1211.76160 Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 369, No. 1935, 371-395 (2011). MSC: 76X05 82D10 PDF BibTeX XML Cite \textit{R. L. Viana} et al., Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 369, No. 1935, 371--395 (2011; Zbl 1211.76160) Full Text: DOI
Seoane, Jesús M.; Sanjuán, Miguel A. F. Escaping dynamics in the presence of dissipation and noise in scattering systems. (English) Zbl 1202.37083 Int. J. Bifurcation Chaos Appl. Sci. Eng. 20, No. 9, 2783-2793 (2010). MSC: 37J99 37N20 37Fxx 37H99 PDF BibTeX XML Cite \textit{J. M. Seoane} and \textit{M. A. F. Sanjuán}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 20, No. 9, 2783--2793 (2010; Zbl 1202.37083) Full Text: DOI
Portela, Jefferson S. E.; Caldas, Iberê L.; Viana, Ricardo L.; Sanjuán, Miguel A. F. Fractal and Wada exit basin boundaries in tokamaks. (English) Zbl 1193.78017 Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, No. 11, 4067-4079 (2007). MSC: 78A55 37D45 37N20 PDF BibTeX XML Cite \textit{J. S. E. Portela} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, No. 11, 4067--4079 (2007; Zbl 1193.78017) Full Text: DOI
Nusse, Helena E.; Yorke, James A. Bifurcations of basins of attraction from the view point of prime ends. (English) Zbl 1118.37028 Topology Appl. 154, No. 13, 2567-2579 (2007). MSC: 37G35 37C70 37E30 PDF BibTeX XML Cite \textit{H. E. Nusse} and \textit{J. A. Yorke}, Topology Appl. 154, No. 13, 2567--2579 (2007; Zbl 1118.37028) Full Text: DOI
Breban, Romulus; Nusse, Helena E. On the creation of Wada basins in interval maps through fixed point tangent bifurcation. (English) Zbl 1093.37012 Physica D 207, No. 1-2, 52-63 (2005). MSC: 37E05 37C10 37G99 PDF BibTeX XML Cite \textit{R. Breban} and \textit{H. E. Nusse}, Physica D 207, No. 1--2, 52--63 (2005; Zbl 1093.37012) Full Text: DOI
Aguirre, Jacobo; Vallejo, Juan Carlos; Sanjuan, Miguel A. F. Wada basins and unpredictability in Hamiltonian and dissipative systems. (English) Zbl 1073.37024 Int. J. Mod. Phys. B 17, No. 22-24, Part 2, 4171-4175 (2003). MSC: 37C70 37D45 PDF BibTeX XML Cite \textit{J. Aguirre} et al., Int. J. Mod. Phys. B 17, No. 22--24, Part 2, 4171--4175 (2003; Zbl 1073.37024) Full Text: DOI
Sun, Yi Sui (ed.); He, Xia Tu (ed.); Sheng, Zheng Mao (ed.) Dynamics Days Asia-Pacific (DDAP). Proceedings of the 2nd international conference on nonlinear science, Hangzhou, China, August 8–12, 2002. (English) Zbl 1072.37502 Int. J. Mod. Phys. B 17, No. 22-24, Part 2, x, 4171-4433 (2003). MSC: 37-06 37Nxx 00B25 PDF BibTeX XML Cite \textit{Y. S. Sun} (ed.) et al., Int. J. Mod. Phys. B 17, No. 22--24, Part 2, x, 4171--4433 (2003; Zbl 1072.37502) Full Text: DOI
Aguirre, Jacobo; Sanjuán, Miguel A. F. Unpredictable behavior in the Duffing oscillator: Wada basins. (English) Zbl 1008.37011 Physica D 171, No. 1-2, 41-51 (2002). MSC: 37C70 37D45 37N10 PDF BibTeX XML Cite \textit{J. Aguirre} and \textit{M. A. F. Sanjuán}, Physica D 171, No. 1--2, 41--51 (2002; Zbl 1008.37011) Full Text: DOI
Vandermeer, John; Stone, Lewi; Blasius, Bernd Categories of chaos and fractal basin boundaries in forced predator-prey models. (English) Zbl 0976.92033 Chaos Solitons Fractals 12, No. 2, 265-276 (2001). MSC: 92D40 37N25 PDF BibTeX XML Cite \textit{J. Vandermeer} et al., Chaos Solitons Fractals 12, No. 2, 265--276 (2001; Zbl 0976.92033) Full Text: DOI
Sanjuán, Miguel A. F. The effect of nonlinear damping on the universal escape oscillator. (English) Zbl 0977.34041 Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, No. 4, 735-744 (1999). Reviewer: Antonio Cañada (Granada) MSC: 34C37 37G15 70K50 34C15 PDF BibTeX XML Cite \textit{M. A. F. Sanjuán}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, No. 4, 735--744 (1999; Zbl 0977.34041) Full Text: DOI
Virgin, L. N.; Todd, M. D.; Begley, C. J.; Trickey, S. T.; Dowell, E. H. Basins of attraction in experimental nonlinear oscillators. (English) Zbl 0936.37014 Int. J. Bifurcation Chaos Appl. Sci. Eng. 8, No. 3, 521-533 (1998). MSC: 37D45 37J40 37J45 PDF BibTeX XML Cite \textit{L. N. Virgin} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 8, No. 3, 521--533 (1998; Zbl 0936.37014) Full Text: DOI