[1] |
Abraham, R. H., Gardini, L. & Mira, C. [1997] Chaos in Discrete Dynamical Systems: A Visual Introduction in 2 Dimensions (Springer-Verlag, NY). · Zbl 0883.58019 |
[2] |
Agliari, A., Gardini, L. & Mira, C. [2003] “ On the fractal structure of basin boundaries in two-dimensional noninvertible maps,” Int. J. Bifurcation and Chaos13, 1767-1785. · Zbl 1056.37058 |
[3] |
Aguirre, J., Viana, R. L. & Sanjuán, M. A. [2009] “ Fractal structures in nonlinear dynamics,” Rev. Mod. Phys.81, 333. |
[4] |
Argyris, J. H., Faust, G., Haase, M. & Friedrich, R. [2015] An Exploration of Dynamical Systems and Chaos, 2nd edition (Springer, Berlin, Heidelberg). · Zbl 1314.37003 |
[5] |
Birkhoff, G. & Rota, G.-C. [1989] Ordinary Differential Equations, 4th edition (Wiley, NY). · Zbl 0183.35601 |
[6] |
Creaser, J. L., Krauskopf, B. & Osinga, H. M. [2017] “ Finding first foliation tangencies in the Lorenz system,” SIAM J. Appl. Dyn. Syst.16, 2127-2164. · Zbl 1381.37097 |
[7] |
Daza, A., Wagemakers, A., Georgeot, B., Guéry-Odelin, D. & Sanjuán, M. A. [2016] “ Basin entropy: A new tool to analyze uncertainty in dynamical systems,” Scient. Rep.6, 1-10. · Zbl 1386.37080 |
[8] |
Dong, Y., Wang, G., Iu, H. H.-C., Chen, G. & Chen, L. [2020] “ Coexisting hidden and self-excited attractors in a locally active memristor-based circuit,” Chaos30, 103123. · Zbl 1466.94059 |
[9] |
Dumortier, F., Llibre, J. & Artés, J. C. [2006] Qualitative Theory of Planar Differential Systems (Springer-Verlag, Berlin, Heidelberg). · Zbl 1110.34002 |
[10] |
Falconer, K. [2004] Fractal Geometry: Mathematical Foundations and Applications (Wiley, NY). · Zbl 1060.28005 |
[11] |
Fenichel, N. [1979] “ Geometric singular perturbation theory for ordinary differential equations,” J. Diff. Eqs.31, 53-98. · Zbl 0476.34034 |
[12] |
Feudel, U. [2008] “ Complex dynamics in multistable systems,” Int. J. Bifurcation and Chaos18, 1607-1626. |
[13] |
Gingold, H. & Solomon, D. [2011] “ The Lorenz system has a global repeller at infinity,” J. Nonlin. Math. Phys.18, 183-189. · Zbl 1221.37033 |
[14] |
Grebogi, C., McDonald, S. W., Ott, E. & Yorke, J. A. [1983] “ Final state sensitivity: An obstruction to predictability,” Phys. Lett. A99, 415-418. |
[15] |
Harne, R. L. & Wang, K.-W. [2017] Harnessing Bistable Structural Dynamics: For Vibration Control, Energy Harvesting and Sensing (Wiley, NY). · Zbl 1358.74002 |
[16] |
Huisman, J. & Weissing, F. J. [2001] “ Fundamental unpredictability in multispecies competition,” The Amer. Natur.157, 488-494. |
[17] |
Katunin, A. [2017] A Concise Introduction to Hypercomplex Fractals (CRC Press, Boca Raton). · Zbl 1377.28009 |
[18] |
Khalil, H. K. & Grizzle, J. W. [2002] Nonlinear Systems, Vol. 3 (Prentice Hall, NJ). · Zbl 1003.34002 |
[19] |
Liu, J., Crawford, J. & Viola, R. [1995] “ Chaos, coexistence of attractors and fractal basin boundaries of attraction in a model system coupling activation and inhibition in parallel,” Dyn. Stab. Syst.10, 111-124. · Zbl 0840.34060 |
[20] |
Lorenz, E. N. [1963] “ Deterministic nonperiodic flow,” J. Atmosph. Sci.20, 130-141. · Zbl 1417.37129 |
[21] |
McDonald, S. W., Grebogi, C., Ott, E. & Yorke, J. A. [1985] “ Fractal basin boundaries,” Physica D17, 125-153. · Zbl 0588.58033 |
[22] |
Munkres, J. [2014] Topology, 2nd edition (Pearson, Edinburgh Gate). · Zbl 0951.54001 |
[23] |
Murdock, J. [2003] Normal Forms and Unfoldings for Local Dynamical Systems (Springer Science & Business Media). · Zbl 1014.37001 |
[24] |
Nusse, H. E. & Yorke, J. A. [2000] “ Fractal basin boundaries generated by basin cells and the geometry of mixing chaotic flows,” Phys. Rev. Lett.84, 626. |
[25] |
Puy, A., Daza, A., Wagemakers, A. & Sanjuán, M. A. [2021] “ A test for fractal boundaries based on the basin entropy,” Commun. Nonlin. Sci. Numer. Simul.95, 105588. · Zbl 1457.37034 |
[26] |
Sparrow, C. [1982] The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors, , Vol. 41 (Springer-Verlag, NY). · Zbl 0504.58001 |
[27] |
Strogatz, S. H. [2018] Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (CRC Press, Boca Raton). |
[28] |
Tucker, W. [1999] “ The Lorenz attractor exists,” Comptes Rendus de l’Académie des Sciences-Series I-Mathematics328, 1197-1202. · Zbl 0935.34050 |
[29] |
Viswanath, D. [2003] “ Symbolic dynamics and periodic orbits of the Lorenz attractor,” Nonlinearity16, 1035-1056. · Zbl 1030.37010 |
[30] |
Wiggins, S. [2003] Introduction to Applied Nonlinear Dynamical Systems and Chaos (Springer Science & Business Media). · Zbl 1027.37002 |