Michael, S.: Applied Nonlinear Time Series Analysis: Applicationsin Physics, Physiology and Finance, vol. 52. World Scientific, Singapore (2005)
Google Scholar
Bradley, E., Kantz, H.: Nonlinear time-series analysis revisited. Chaos Interdiscipl. J. Nonlinear Sci. 25(9), 097610 (2015)
MathSciNet
MATH
Google Scholar
Scheffer, M., Bascompte, J., Brock, W.A., Brovkin, V., Carpenter, S.R., Dakos, V., Held, H., Van Nes, E.H., Rietkerk, M., Sugihara, G.: Early-warning signals for critical transitions. Nature 461(7260), 53 (2009)
Google Scholar
Marwan, N., Schinkel, S., Kurths, J.: In: Proceedings of the 2008 International Symposium on Nonlinear Theory and its Applications NOLTA08, Budapest, Hungary (2008), pp. 412–415
Donges, J.F., Donner, R., Marwan, N., Breitenbach, S.F., Rehfeld, K., Kurths, J.: Non-linear regime shifts in Holocene Asian monsoon variability: potential impacts on cultural change and migratory patterns. Clim. Past 11(5), 709 (2015)
Google Scholar
Donges, J.F., Donner, R.V., Rehfeld, K., Marwan, N., Trauth, M.H., Kurths, J.: Identification of dynamical transitions in marine palaeoclimate records by recurrence network analysis. Nonlinear Process. Geophys. 18(5), 545 (2011)
Google Scholar
Malik, N., Zou, Y., Marwan, N., Kurths, J.: Dynamical regimes and transitions in Plio-Pleistocene Asian monsoon. EPL (Europhysics Letters). 97(4), 40009 (2012)
Google Scholar
Smirnov, D., Breitenbach, S., Feulner, G., Lechleitner, F., Prufer, K., Baldini, J., Marwan, N., Kurths, J.: A regime shift in the Sun-Climate connection with the end of the Medieval Climate Anomaly. Sci. Rep. 7(1), 11131 (2017)
Google Scholar
Chen, Y., Yang, H.: Heterogeneous recurrence representation and quantification of dynamic transitions in continuous nonlinear processes. Eur. Phys. J. B 89(6), 155 (2016)
Google Scholar
Unni, V.R., Sujith, R.I.: Multifractal characteristics of combustor dynamics close to lean blowout. J. Fluid Mech. 784, 30 (2015)
Google Scholar
Godavarthi, V., Unni, V.R., Gopalakrishnan, E., Sujith, R.I.: Recurrence networks to study dynamical transitions in a turbulent combustor. Chaos Interdiscipl. J. Nonlinear Sci. 27(6), 063113 (2017)
Google Scholar
Marwan, N., Eroglu, D., Ozken, I., Stemler, T., Wyrwoll, K.H., Kurths, J.: In:Advances in Nonlinear Geosciences (Springer, 2018), pp. 357–368
Goswami, B., Boers, N., Rheinwalt, A., Marwan, N., Heitzig, J., Breitenbach, S.F., Kurths, J.: Abrupt transitions in time series with uncertainties. Nat. Commun. 9(1), 48 (2018)
Google Scholar
Marwan, N., Wessel, N., Meyerfeldt, U., Schirdewan, A., Kurths, J.: Recurrence-plot-based measures of complexity and their application to heart-rate-variability data. Phys. Rev. E 66(2), 026702 (2002)
MATH
Google Scholar
Prado, TdL, Lopes, S., Batista, C., Kurths, J., Viana, R.: Synchronization of bursting Hodgkin-Huxley-type neurons in clustered networks. Phys. Rev. E 90(3), 032818 (2014)
Google Scholar
Izhikevich, E.M.: Dynamical Systems in Neuroscience. MIT Press, Cambridge (2007)
Google Scholar
Venegas, J.G., Winkler, T., Musch, G., Melo, M.F.V., Layfield, D., Tgavalekos, N., Fischman, A.J., Callahan, R.J., Bellani, G., Harris, R.S.: Self-organized patchiness in asthma as a prelude to catastrophic shifts. Nature 434(7034), 777 (2005)
Google Scholar
Mantegna, R.N., Stanley, H.E.: Introduction to Econophysics: Correlations and Complexity in Finance. Cambridge University Press, Cambridge (1999)
MATH
Google Scholar
Fabretti, A., Ausloos, M.: Recurrence plot and recurrence quantification analysis techniques for detecting a critical regime. Examples from financial market inidices. Int. J. Mod. Phys. C 16(05), 671 (2005)
MATH
Google Scholar
Malik, N., Marwan, N., Zou, Y., Mucha, P.J., Kurths, J.: Fluctuation of similarity to detect transitions between distinct dynamical regimes in short time series. Phys. Rev. E 89(6), 062908 (2014)
Google Scholar
Krishnan, A., Sujith, R.I., Marwan, N., Kurths, J.: On the emergence of large clusters of acoustic power sources at the onset of thermoacoustic instability in a turbulent combustor. J. Fluid Mech. 874, 455 (2019)
MathSciNet
MATH
Google Scholar
Kantelhardt, J.W., Zschiegner, S.A., Koscielny-Bunde, E., Havlin, S., Bunde, A., Stanley, H.E.: Multifractal detrended fluctuation analysis of nonstationary time series. Physica A 316(1–4), 87 (2002)
MATH
Google Scholar
Letellier, C.: Estimating the Shannon entropy: recurrence plots versus symbolic dynamics. Phys. Rev. Lett. 96(25), 254102 (2006)
Google Scholar
Eckmann, J., Kamphorst, S.O., Ruelle, D., et al.: Recurrence plots of dynamical systems. World Sci. Ser Nonlinear Sci. Ser. A 16, 441 (1995)
Google Scholar
Poincaré, H.: Sur le problème des trois corps et les équations de la dynamique. Acta Math. 13(1), A3 (1890)
Google Scholar
Marwan, N.: A historical review of recurrence plots. Eur. Phys. J. Special Top. 164(1), 3 (2008)
MathSciNet
Google Scholar
Marwan, N., Romano, M.C., Thiel, M., Kurths, J.: Recurrence plots for the analysis of complex systems. Phys. Rep. 438(5–6), 237 (2007)
MathSciNet
Google Scholar
Corso, G., Prado, TdL, Lima, GZdS, Kurths, J., Lopes, S.R.: Quantifying entropy using recurrence matrix microstates. Chaos Interdiscip. J. Nonlinear Sci. 28(8), 083108 (2018)
MathSciNet
MATH
Google Scholar
Mandelbrot, B.B.: The Fractal Geometry of Nature, vol. 173. WH freeman, New York (1983)
Google Scholar
Plotnick, R.E., Gardner, R.H., Hargrove, W.W., Prestegaard, K., Perlmutter, M.: Lacunarity analysis: a general technique for the analysis of spatial patterns. Phys. Rev. E 53(5), 5461 (1996)
Google Scholar
Cheng, Q.: Multifractal modeling and lacunarity analysis. Math. Geol. 29(7), 919 (1997)
Google Scholar
Jacob, R., Harikrishnan, K., Misra, R., Ambika, G.: Measure for degree heterogeneity in complex networks and its application to recurrence network analysis. Roy. Soc. Open Sci. 4(1), 160757 (2017)
MathSciNet
Google Scholar
Malhi, Y., Román-Cuesta, R.M.: Analysis of lacunarity and scales of spatial homogeneity in IKONOS images of Amazonian tropical forest canopies. Remote Sens. Environ. 112(5), 2074 (2008)
Google Scholar
Gomides, A.V.M., de Paula Gonçalves, L.J., Silva, L.R., Backes, A.R.: In: 2018 7th Brazilian Conference on Intelligent Systems (BRACIS) (IEEE, 2018), pp. 307–311
Marwan, N., Saparin, P., Kurths, J.: Measures of complexity for 3D image analysis of trabecular bone. Eur. Phys. J. Special Top. 143(1), 109 (2007)
Google Scholar
Gaite, J.: Fractal analysis of the large-scale stellar mass distribution in the Sloan Digital Sky Survey. J. Cosmol. Astropart. Phys. 2018(07), 010 (2018)
Google Scholar
Karperien, A., Jelinek, H., Milosevic, N., Cracow, P.: In: 8th European Conference on Mathematical and Theoretical Biology (2011)
Tony, J., Gopalakrishnan, E., Sreelekha, E., Sujith, R.I.: Detecting deterministic nature of pressure measurements from a turbulent combustor. Phys. Rev. E 92(6), 062902 (2015)
Google Scholar
Takens, F.: In: Dynamical systems and turbulence Warwick 1980. Springer 1981, pp. 366–381
Cao, L.: Practical method for determining the minimum embedding dimension of a scalar time series. Physica D 110(1–2), 43 (1997)
MATH
Google Scholar
Pecora, L.M., Moniz, L., Nichols, J., Carroll, T.L.: A unified approach to attractor reconstruction. Chaos Interdiscip. J. Nonlinear Sci. 17(1), 013110 (2007)
MathSciNet
MATH
Google Scholar
Kantz, H.: A robust method to estimate the maximal Lyapunov exponent of a time series. Phys. Lett. A 185(1), 77 (1994)
Google Scholar
Webber Jr, C.L., Marwan, N.: Theory and Best Practices (2015)
Marwan, N.: How to avoid potential pitfalls in recurrence plot based data analysis. Int. J. Bifurcat. Chaos 21(04), 1003 (2011)
MathSciNet
MATH
Google Scholar
Kraemer, K.H., Marwan, N.: Border effect corrections for diagonal line based recurrence quantification analysis measures. Phys. Lett. A 383(34), 125977 (2019)
MathSciNet
Google Scholar
Quan, Y., Xu, Y., Sun, Y., Luo, Y.: Proceedings of the IEEE Conference On Computer Vision and Pattern Recognition, pp. 160–167 (2014)
Karperien, A.L., Jelinek, H.F.: The Fractal Geometry of the Brain, pp. 13–43. Springer, New York (2016)
Google Scholar
Dong, P.: Test of a new lacunarity estimation method for image texture analysis. Int. J. Remote Sens. 21(17), 3369 (2000)
Google Scholar
Ivanovici, M., Richard, N., Decean, H.: Fractal dimension and lacunarity of psoriatic lesions-a colour approach. Medicine 6(4), 7 (2009)
Google Scholar
Allain, C., Cloitre, M.: Characterizing the lacunarity of random and deterministic fractal sets. Phys. Rev. A 44(6), 3552 (1991)
MathSciNet
Google Scholar
Alber, M., Peinke, J.: Improved multifractal box-counting algorithm, virtual phase transitions, and negative dimensions. Phys. Rev. E 57(5), 5489 (1998)
Google Scholar
Feagin, R., Wu, X., Feagin, T.: Edge effects in lacunarity analysis. Ecol. Model. 201(3–4), 262 (2007)
Google Scholar
Valous, N., Xiong, W., Halama, N., Zörnig, I., Cantre, D., Wang, Z., Nicolai, B., Verboven, P., Moraleda, R Rojas: Multilacunarity as a spatial multiscale multi-mass morphometric of change in the meso-architecture of plant parenchyma tissue. Chaos Interdiscip. J. Nonlinear Sci. 28(9), 093110 (2018)
Google Scholar
Bacry, E., Delour, J., Muzy, J.F.: Multifractal random walk. Phys. Rev. E 64(2), 026103 (2001)
MATH
Google Scholar
Babinec, P., Kučera, M., Babincová, M.: Global characterization of time series using fractal dimension of corresponding recurrence plots: from dynamical systems to heart physiology. Harmon Fractal Image Anal. 1, 87 (2005)
Google Scholar
Lin, B., Yang, Z.: A suggested lacunarity expression for Sierpinski carpets. J. Phys. A: Math. Gen. 19(2), L49 (1986)
MATH
Google Scholar
Webber, C.: Recurrence quantification of fractal structures. Front. Physiol. 3, 382 (2012)
Google Scholar
Donner, R.V., Heitzig, J., Donges, J.F., Zou, Y., Marwan, N., Kurths, J.: The geometry of chaotic dynamics a complex network perspective. Eur. Phys. J. B 84(4), 653 (2011)
MathSciNet
Google Scholar
Tibshirani, R.J., Efron, B.: An introduction to the bootstrap. Monograph Stat. Appl. Probabil. 57, 1 (1993)
MathSciNet
MATH
Google Scholar
Lancaster, G., Iatsenko, D., Pidde, A., Ticcinelli, V., Stefanovska, A.: Surrogate data for hypothesis testing of physical systems. Phys. Rep. 748, 1 (2018)
MathSciNet
MATH
Google Scholar
Marwan, N., Schinkel, S., Kurths, J.: Recurrence plots 25 years later-Gaining confidence in dynamical transitions. EPL (Europhysics Letters) 101(2), 20007 (2013)
Google Scholar
Ott, E.: Chaos in Dynamical Systems. Cambridge University Press, Cambridge (2002)
MATH
Google Scholar
Aballe, A., Bethencourt, M., Botana, F., Marcos, M.: Using wavelets transform in the analysis of electrochemical noise data. Electrochim. Acta 44(26), 4805 (1999)
Google Scholar
Kalmykov, Y.P., Coffey, W., Titov, S.: On the Brownian motion in a double-well potential in the overdamped limit. Physica A 377(2), 412 (2007)
Google Scholar
Gammaitoni, L., Hänggi, P., Jung, P., Marchesoni, F.: Stochastic Resonance. Rev. Mod. Phys. 70(1), 223 (1998)
Google Scholar
Ashwin, P., Wieczorek, S., Vitolo, R., Cox, P.: Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system. Philosoph. Trans. R Soc. A Math. Phys. Eng. Sci. 370(1962), 1166 (2012)
Google Scholar
Kasthuri, P., Pavithran, I., Pawar, S.A., Sujith, R.I., Gejji, R., Anderson, W.: Dynamical systems approach to study thermoacoustic transitions in a liquid rocket combustor. Chaos Interdiscip. J. Nonlinear Sci. 29(10), 103115 (2019)
Google Scholar
Unni, V.R., Krishnan, A., Manikandan, R., George, N.B., Sujith, R.I., Marwan, N., Kurths, J.: On the emergence of critical regions at the onset of thermoacoustic instability in a turbulent combustor. Chaos Interdiscip. J. Nonlinear Sci. 28(6), 063125 (2018)
MathSciNet
Google Scholar
Nair, V., Thampi, G., Sujith, R.I.: Intermittency route to thermoacoustic instability in turbulent combustors. J. Fluid Mech. 756, 470 (2014)
Google Scholar
Godavarthi, V., Pawar, S.A., Unni, V.R., Sujith, R.I., Marwan, N., Kurths, J.: Coupled interaction between unsteady flame dynamics and acoustic field in a turbulent combustor. Chaos Interdiscip. J. Nonlinear Sci. 28(11), 113111 (2018)
MathSciNet
Google Scholar
Sujith, R.I., Unni, V.R.: Complex system approach to investigate and mitigate thermoacoustic instability in turbulent combustors. Phys. Fluids 32(6), 061401 (2020)
Google Scholar
Ye, Q., Xia, Y., Yao, Z.: Classification of gait patterns in patients with neurodegenerative disease using adaptive neuro-fuzzy inference system. Computational and mathematical methods in medicine 2018, (2018)