References
- [1] A. Hastings, C.L. Hom, S. Ellner, P. Turchin, H.C.J. Godfray, Chaos in Ecology: Is Mother Nature a Strange Attractor?, Annu. Rev. Ecol. Syst. 24 (1993), 1–33.10.1146/annurev.es.24.110193.000245
- [2] D. Rickles, P. Hawe, A. Shiell, A Simple Guide to Chaos and Complexity, J. Epidemiol. Commun. Health. 61 (2007), 933–937.10.1136/jech.2006.054254246560217933949
- [3] M. Berezowski, M. Lawnik, Identification of fast-changing signals by means of adaptive chaotic transformations, Nonlinear Anal. Model. Control, 19 (2014), 172–177.10.15388/NA.2014.2.2
- [4] M. Lawnik, M. Berezowski, Identification of the oscillation period of chemical reactors by chaotic sampling of the conversion degree, Chem. Process Eng. 35 (2014), 387–393.10.2478/cpe-2014-0029
- [5] M. Lawnik, Generation of numbers with the distribution close to uniform with the use of chaotic maps, Proceedings of the 4th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, (2014), 451–455.10.5220/0005090304510455
- [6] S. Kumari, R. Chugh, J. Cao, C. Huang, On the construction, properties and Hausdorff dimension of random Cantor one pth set, AIMS Mathematics, 5 (2020), 3138–3155.10.3934/math.2020202
- [7] S. Kumari, R. Chugh, J. Cao, C. Huang, Multi Fractals of Generalized Multivalued Iterated Function Systems in b-Metric Spaces with Applications, Mathematics 7 (2019), 967.10.3390/math7100967
- [8] S. Kumari, R. Chugh, Novel fractals of Hutchinson Barnsley operator in Hausdorff g-metric spaces, Poincare Journal of Analysis & Applications, 7 (2020), 99–117.10.46753/pjaa.2020.v07i01.010
- [9] S. Kumari, M. Kumari, R. Chugh, Dynamics of superior fractals via Jungck SP orbit with s-convexity, Annals of the University of Craiova-Mathematics and Computer Science Series, 46(2), 2019, 344–365.
- [10] S. Kumari, M. Kumari, R. Chugh, Graphics for complex polynomials in Jungck-SP orbit, IAENG International Journal of Applied Mathematics, 49 (2019), 568–576.
- [11] R.L. Devaney, An Introduction to Chaotic Dynamical Systems, 2nd ed., Westview Press, USA 2003.
- [12] K.T. Alligood, T.D. Sauer, J.A. Yorke, Chaos : An Introduction to Dynamical Systems, Springer, New York 1996.10.1007/b97589
- [13] R.A. Holmgren, A first course in discrete dynamical systems, Springer-Verlag; 1994.10.1007/978-1-4684-0222-3
- [14] R. May, Simple mathematical models with very complicated dynamics, Nature, 261 (1976), 459–475.10.1038/261459a0934280
- [15] S. Kumar, M. Kumar, R. Budhiraja, M.K. Das, S. Singh, A secured cryptographic model using intertwining logistic map, Procedia Computer Science, 143 (2018), 804–811.10.1016/j.procs.2018.10.386
- [16] C. Han, An image encryption algorithm based on modified logistic chaotic map, Optik, 181 (2019), 779-785.10.1016/j.ijleo.2018.12.178
- [17] Z. Hua, Y. Zhou, Image encryption using 2D Logistic-adjusted-Sine map, Inf. Sci. 339 (2016), 237–253.10.1016/j.ins.2016.01.017
- [18] L.P.L. de Oliveira, M. Sobottka, Cryptography with chaotic mixing, Chaos, Solitons & Fractals, 3 (2008), 466–471.10.1016/j.chaos.2006.05.049
- [19] P. Shang, X. Li, S. Kame, Chaotic analysis of traffic time series, Chaos, Solitons & Fractals, 25 (2005), 121–128.10.1016/j.chaos.2004.09.104
- [20] S.C. Lo, H.J. Cho, Chaos and control of discrete dynamic traffic model, J. Franklin Inst. 342 (2005), 839–851.10.1016/j.jfranklin.2005.06.002
- [21] M. McCartney, A discrete time car following model and the bi-parameter logistic map, Commun. Nonlinear Sci. Numer. Simul. 14 (2009), 233–243.10.1016/j.cnsns.2007.06.012
- [22] Ashish, J. Cao, R. Chugh, Chaotic behavior of logistic map in superior orbit and an improved chaos-based traffic control model, Nonlinear Dynamics, 2018, 1–17. https://doi.org/10.1007/s11071-018-4403-y.10.1007/s11071-018-4403-y
- [23] T. Nagatani, Vehicular motion through a sequence of traffic lights controlled by logistic map, Physics Letters A, 372 (2008), 5887–5890.10.1016/j.physleta.2008.07.063
- [24] T. Nagatani, N. Sugiyama, Vehicular traffic flow through a series of signals with cycle time generated by a logistic map, Physica A, 392 (2013), 851–856.10.1016/j.physa.2012.10.015
- [25] S. Kumari, R. Chugh, A novel four-step feedback procedure for rapid control of chaotic behavior of the logistic map and unstable traffic on the road, Chaos, 30 (2020), 123115.10.1063/5.0022212
- [26] N. Singh, A. Sinha, Chaos-based secure communication system using logistic map, Opt. Lasers Eng. 48 (2010), 398–404.10.1016/j.optlaseng.2009.10.001
- [27] J.S. Martin, M.A. Porter, Convergence time towards periodic orbits in discrete dynamical systems, PLOS One, 9 (2014), 1–9.
- [28] R.V. Medina, A.D. Mendez, J.L. Rio-Correa, J.L. Hernandez, Design of chaotic analog noise generators with logistic map and MOS QT circuits, Chaos, Solitons & Fractals, 40 (2009), 1779–1793.10.1016/j.chaos.2007.09.088
- [29] R. Chugh, A. Kumar, S. Kumari, A novel epidemic model to analyze and control the chaotic behavior of covid-19 outbreak, Bulletin of the Transilvania University of Brasov, Series III: Mathematics, Informatics, Physics, 13(2020), 479-508.
- [30] F.G. Xie, B.L. Hao, ymbolic Dynamics of the Sine-square Map, Chaos, Solitons & Fractals, 3 (1993), 47-60.10.1016/0960-0779(93)90039-4
- [31] P. Philominathan, P. Neelamegam, S. Rajasekar, Statistical dynamics of sine-square map, Physica A, 242 (1997), 391–408.10.1016/S0378-4371(97)00259-8
- [32] B. Saha, S.T. Malasani, J.B. Seventline, Application of Modified Chaotic Sine Map in Secure Communication, Int. J. Comput. Appl. 113 (2015), 9–14.
- [33] H. Ogras, M. Turk, A Secure Chaos-based Image Cryptosystem with an Improved Sine Key Generator, American Journal of Signal Processing, 6 (2016), 67–76.
- [34] X. Jie1, C. Pascal, F.P. Daniele, T.A. Kaddous, L. KePing, Chaos generator for secure transmission using a sine map and an RLC series circuit, Science in China Series F: Information Sciences, 53 (2010), 129–136.10.1007/s11431-010-0024-5
- [35] G.C. Wu, D. Baleanu, S.D. Zeng, Discrete chaos in fractional sine and standard maps, Physics Letters A, 378 (2014), 484–487.10.1016/j.physleta.2013.12.010
- [36] Egydio de Carvalho R., Edson D. Leonel: Squared sine logistic map, Physica A, 463 (2016), 37–44.10.1016/j.physa.2016.07.008
- [37] J. Wu, X. Liao, B. Yang, Image Encryption Using 2D Henon-Sine Map and DNA Approach, Signal Process. 153 (2018), 11–23, doi: 10.1016/j.sigpro.2018.06.008.10.1016/j.sigpro.2018.06.008
- [38] Z. Hua, F. Jin, B. Xu, H. Huang, 2D Logistic-Sine-Coupling Map for Image Encryption, Signal Process. 149 (2018), 148–161, doi: 10.1016/j.sigpro.2018.03.010.10.1016/j.sigpro.2018.03.010
- [39] W.R. Mann, Mean value methods in iteration, Proc. Am. Math. Soc. 4 (1953), 506–510.10.1090/S0002-9939-1953-0054846-3
- [40] M. Rani, R. Agarwal, A new experimental approach to study the stability of logistic map, Chaos, Solitons & Fractals, 41 (2009), 2062–2066.10.1016/j.chaos.2008.08.022
- [41] Ashish, J. Cao, A Novel Fixed Point Feedback Approach Studying the Dynamical Behaviors of Standard Logistic Map, Internat. J. Bifur. Chaos 29(2019), 1950010 (16 pages).10.1142/S021812741950010X
- [42] J. Fridrich, Image encryption based on chaotic maps, in Proceedings of IEEE International Conference on Systems, Man and Cybernetics(ICSMC‘97), 2(1997), 1105–1110.