Vortkamp, Irina; Schreiber, Sebastian J.; Hastings, Alan; Hilker, Frank M. Multiple attractors and long transients in spatially structured populations with an Allee effect. (English) Zbl 1453.92267 Bull. Math. Biol. 82, No. 6, Paper No. 82, 21 p. (2020). MSC: 92D25 34C23 PDF BibTeX XML Cite \textit{I. Vortkamp} et al., Bull. Math. Biol. 82, No. 6, Paper No. 82, 21 p. (2020; Zbl 1453.92267) Full Text: DOI
Yue, Xiaole; Xu, Wei; Zhang, Ying; Du, Lin Analysis of global properties for dynamical systems by a modified digraph cell mapping method. (English) Zbl 1398.65342 Chaos Solitons Fractals 111, 206-212 (2018). MSC: 65P20 34D45 PDF BibTeX XML Cite \textit{X. Yue} et al., Chaos Solitons Fractals 111, 206--212 (2018; Zbl 1398.65342) Full Text: DOI
Gan, C. B. Fractal basin boundaries and chaotic dynamics in the randomly-driven Henon-Heiles oscillator. (English) Zbl 1225.70013 Zhu, W. Q. (ed.) et al., IUTAM symposium on nonlinear stochastic dynamics and control. Proceedings of the IUTAM symposium held in Hangzhou, China, May 10–14, 2010. Dordrecht: Springer (ISBN 978-94-007-0731-3/hbk; 978-94-007-0732-0/ebook). IUTAM Bookseries 29, 183-190 (2011). MSC: 70H06 PDF BibTeX XML Cite \textit{C. B. Gan}, IUTAM Bookser. 29, 183--190 (2011; Zbl 1225.70013) Full Text: DOI
Akroune, Nourredine On the fractal dimension of a nowhere differentiable basin boundary. (English) Zbl 1224.65295 Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 54(102), No. 1, 3-13 (2011). MSC: 65P40 37M25 28A80 37L30 PDF BibTeX XML Cite \textit{N. Akroune}, Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 54(102), No. 1, 3--13 (2011; Zbl 1224.65295)
Narayaninsamy, T. A method to construct irregular fractal curves. (English) Zbl 1193.28009 Appl. Math. Comput. 192, No. 1, 260-273 (2007). MSC: 28A80 37C99 PDF BibTeX XML Cite \textit{T. Narayaninsamy}, Appl. Math. Comput. 192, No. 1, 260--273 (2007; Zbl 1193.28009) Full Text: DOI
Gan, Chunbiao; Cheng, Xiaoyin Noise-induced fractal boundary of safe basin in the softening Duffing oscillator. (English) Zbl 1129.34038 Dyn. Contin. Discrete Impuls. Syst., Ser. B, Appl. Algorithms 14, No. 4, 525-536 (2007). Reviewer: Henri Schurz (Carbondale) MSC: 34F05 93E25 34C15 34D45 60H10 65C05 65C30 PDF BibTeX XML Cite \textit{C. Gan} and \textit{X. Cheng}, Dyn. Contin. Discrete Impuls. Syst., Ser. B, Appl. Algorithms 14, No. 4, 525--536 (2007; Zbl 1129.34038)
Gan, Chunbiao Noise-induced chaos in Duffing oscillator with double wells. (English) Zbl 1123.70021 Nonlinear Dyn. 45, No. 3-4, 305-317 (2006). MSC: 70K55 70L05 PDF BibTeX XML Cite \textit{C. Gan}, Nonlinear Dyn. 45, No. 3--4, 305--317 (2006; Zbl 1123.70021) Full Text: DOI
Tyrkiel, Elżbieta On the role of chaotic saddles in generating chaotic dynamics in nonlinear driven oscillators. (English) Zbl 1089.37030 Int. J. Bifurcation Chaos Appl. Sci. Eng. 15, No. 4, 1215-1238 (2005). MSC: 37D45 37G25 34C15 34C23 34C37 PDF BibTeX XML Cite \textit{E. Tyrkiel}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 15, No. 4, 1215--1238 (2005; Zbl 1089.37030) Full Text: DOI
Hong, Ling; Xu, Jianxue A chaotic crisis between chaotic saddle and attractor in forced Duffing oscillators. (English) Zbl 1046.34071 Commun. Nonlinear Sci. Numer. Simul. 9, No. 3, 313-329 (2004). MSC: 34C28 34C15 PDF BibTeX XML Cite \textit{L. Hong} and \textit{J. Xu}, Commun. Nonlinear Sci. Numer. Simul. 9, No. 3, 313--329 (2004; Zbl 1046.34071) Full Text: DOI
Sil’chenko, A. N.; Beri, S.; Luchinskij, D. G.; McClintock, P. V. E. Fluctuational transitions across locally disconnected and locally connected fractal basin boundaries. (English) Zbl 1048.37524 Izv. Vyssh. Uchebn. Zaved., Prikl. Nelinejn. Din. 11, No. 3, 38-43 (2003). Reviewer: Mikhail Kalugin (Moskva) MSC: 37N20 37G35 37E30 35Q40 81Q05 PDF BibTeX XML Cite \textit{A. N. Sil'chenko} et al., Izv. Vyssh. Uchebn. Zaved., Prikl. Nelineĭn. Din. 11, No. 3, 38--43 (2003; Zbl 1048.37524)
Nusse, Helena E.; Yorke, James A. Characterizing the basins with the most entangled boundaries. (English) Zbl 1058.37020 Ergodic Theory Dyn. Syst. 23, No. 3, 895-906 (2003). Reviewer: Eugene Ershov (St. Petersburg) MSC: 37C70 37D05 37E30 PDF BibTeX XML Cite \textit{H. E. Nusse} and \textit{J. A. Yorke}, Ergodic Theory Dyn. Syst. 23, No. 3, 895--906 (2003; Zbl 1058.37020) Full Text: DOI
Hong, Ling; Xu, Jianxue Chaotic saddles in Wada basin boundaries and their bifurcations by the generalized cell-mapping digraph (GCMD) method. (English) Zbl 1081.70506 Nonlinear Dyn. 32, No. 4, 371-385 (2003). MSC: 70K55 70K50 PDF BibTeX XML Cite \textit{L. Hong} and \textit{J. Xu}, Nonlinear Dyn. 32, No. 4, 371--385 (2003; Zbl 1081.70506) Full Text: DOI
Breban, Romulus; Nusse, Helena E.; Ott, Edward Lack of predictability in dynamical systems with drift: scaling of indeterminate saddle-node bifurcations. (English) Zbl 1039.37027 Phys. Lett., A 319, No. 1-2, 79-84 (2003). MSC: 37G15 37G35 PDF BibTeX XML Cite \textit{R. Breban} et al., Phys. Lett., A 319, No. 1--2, 79--84 (2003; Zbl 1039.37027) Full Text: DOI
Feudel, U.; Kraut, S. Complex dynamics in multistable systems. (English) Zbl 0960.37012 Fiedler, B. (ed.) et al., International conference on differential equations. Proceedings of the conference, Equadiff ’99, Berlin, Germany, August 1-7, 1999. Vol. 2. Singapore: World Scientific. 1060-1065 (2000). MSC: 37D45 37H20 37C70 PDF BibTeX XML Cite \textit{U. Feudel} and \textit{S. Kraut}, in: International conference on differential equations. Proceedings of the conference, Equadiff '99, Berlin, Germany, August 1--7, 1999. Vol. 2. Singapore: World Scientific. 1060--1065 (2000; Zbl 0960.37012)
Rynio, R.; Okniński, A. Symmetry breaking and fractal dependence on initial conditions in dynamical systems: Ordinary differential equations of thermal convection. (English) Zbl 0942.76016 Chaos Solitons Fractals 9, No. 10, 1723-1732 (1998). Reviewer: Iuliana Oprea (Fort Collins) MSC: 76E06 37N10 34D35 PDF BibTeX XML Cite \textit{R. Rynio} and \textit{A. Okniński}, Chaos Solitons Fractals 9, No. 10, 1723--1732 (1998; Zbl 0942.76016) Full Text: DOI
Jiang, Jun; Xu, Jianxue An iterative method of point mapping under cell reference for the global analysis: Theory and a multiscale reference technique. (English) Zbl 0909.70004 Nonlinear Dyn. 15, No. 2, 103-114 (1998). MSC: 70-08 70K40 37C70 PDF BibTeX XML Cite \textit{J. Jiang} and \textit{J. Xu}, Nonlinear Dyn. 15, No. 2, 103--114 (1998; Zbl 0909.70004) Full Text: DOI
Cui, Fangsen; Chew, C. H.; Xu, Jianxue; Cai, Yuanli Bifurcation and chaos in the Duffing oscillator with a PID controller. (English) Zbl 0881.70014 Nonlinear Dyn. 12, No. 3, 251-262 (1997). MSC: 70K50 37D45 37G99 PDF BibTeX XML Cite \textit{F. Cui} et al., Nonlinear Dyn. 12, No. 3, 251--262 (1997; Zbl 0881.70014) Full Text: DOI
Soliman, Mohamed S. Jump phenomena resulting in unpredictable dynamics in the driven damped pendulum. (English) Zbl 0869.70016 Int. J. Non-Linear Mech. 31, No. 2, 167-174 (1996). MSC: 70K40 PDF BibTeX XML Cite \textit{M. S. Soliman}, Int. J. Non-Linear Mech. 31, No. 2, 167--174 (1996; Zbl 0869.70016) Full Text: DOI
Nusse, Helena E.; Yorke, James A. Wada basin boundaries and basin cells. (English) Zbl 0886.58072 Physica D 90, No. 3-4, 242-261 (1996). MSC: 37D45 37B99 PDF BibTeX XML Cite \textit{H. E. Nusse} and \textit{J. A. Yorke}, Physica D 90, No. 3--4, 242--261 (1996; Zbl 0886.58072) Full Text: DOI
Dobson, I.; Delchamps, D. F. Truncated fractal basin boundaries in the pendulum with nonperiodic forcing. (English) Zbl 0802.58042 J. Nonlinear Sci. 4, No. 4, 315-328 (1994). MSC: 37D45 70K40 PDF BibTeX XML Cite \textit{I. Dobson} and \textit{D. F. Delchamps}, J. Nonlinear Sci. 4, No. 4, 315--328 (1994; Zbl 0802.58042) Full Text: DOI
Lansbury, A. N.; Thompson, J. M. T.; Stewart, H. B. Basin erosion in the twin-well Duffing oscillator: Two distinct bifurcation scenarios. (English) Zbl 0878.34034 Int. J. Bifurcation Chaos Appl. Sci. Eng. 2, No. 3, 505-532 (1992). MSC: 34C23 37D45 34C15 34D45 PDF BibTeX XML Cite \textit{A. N. Lansbury} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 2, No. 3, 505--532 (1992; Zbl 0878.34034) Full Text: DOI
Nusse, Helena E.; Yorke, James A. The equality of fractal dimension and uncertainty dimension for certain dynamical systems. (English) Zbl 0770.58030 Commun. Math. Phys. 150, No. 1, 1-21 (1992). Reviewer: E.Petrisor (Timişoara) MSC: 37D99 28A78 37D45 PDF BibTeX XML Cite \textit{H. E. Nusse} and \textit{J. A. Yorke}, Commun. Math. Phys. 150, No. 1, 1--21 (1992; Zbl 0770.58030) Full Text: DOI
Thompson, J. M. T.; Soliman, M. S. Fractal control boundaries of driven oscillators and their relevance to safe engineering design. (English) Zbl 0692.70032 Proc. R. Soc. Lond., Ser. A 428, No. 1874, 1-13 (1990). MSC: 70Q05 70K50 93B99 PDF BibTeX XML Cite \textit{J. M. T. Thompson} and \textit{M. S. Soliman}, Proc. R. Soc. Lond., Ser. A 428, No. 1874, 1--13 (1990; Zbl 0692.70032) Full Text: DOI
Thompson, J. M. T.; Ueda, Y. Basin boundary metamorphoses in the canonical escape equation. (English) Zbl 0681.70029 Dyn. Stab. Syst. 4, No. 3-4, 285-294 (1989). MSC: 70K50 37D45 70K20 70-08 PDF BibTeX XML Cite \textit{J. M. T. Thompson} and \textit{Y. Ueda}, Dyn. Stab. Syst. 4, No. 3--4, 285--294 (1989; Zbl 0681.70029) Full Text: DOI
Grebogia, Celso; Nusse, Helena E.; Ott, Edward; Yorke, James A. Basic sets: Sets that determine the dimension of basin boundaries. (English) Zbl 0674.58031 Dynamical systems, Proc. Spec. Year, College Park/Maryland, Lect. Notes Math. 1342, 220-250 (1988). Reviewer: N.Ivanov MSC: 37D99 PDF BibTeX XML
Peitgen, H.-O.; Prüfer, M.; Schmitt, K. Global aspects of the continuous and discrete Newton method: A case study. (English) Zbl 0669.65038 Acta Appl. Math. 13, No. 1-2, 123-202 (1988). Reviewer: E.Allgower MSC: 65H10 28A75 65L10 37C10 PDF BibTeX XML Cite \textit{H. O. Peitgen} et al., Acta Appl. Math. 13, No. 1--2, 123--202 (1988; Zbl 0669.65038) Full Text: DOI
Grebogi, Celso; Ott, Edward; Yorke, James A. Basin boundary metamorphoses: Changes in accessible boundary orbits. (English) Zbl 0613.58018 Physica D 24, 243-262 (1987). Reviewer: R.Devaney MSC: 37B99 37N99 28A75 26A18 PDF BibTeX XML Cite \textit{C. Grebogi} et al., Physica D 24, 243--262 (1987; Zbl 0613.58018) Full Text: DOI
Pelikan, Steve A dynamical meaning of fractal dimension. (English) Zbl 0636.58024 Trans. Am. Math. Soc. 292, 695-703 (1985). Reviewer: A.Boyarsky MSC: 37D45 PDF BibTeX XML Cite \textit{S. Pelikan}, Trans. Am. Math. Soc. 292, 695--703 (1985; Zbl 0636.58024) Full Text: DOI