Vasiliy Ye. Belozyorov, Yevhen V. Koshel, Vadym G. Zaytsev


Robust chaos is determined by the absence of periodic windows in bifurcation
diagrams and coexisting attractors with parameter values taken from some regions of the parameter space of a dynamical system. Reliable chaos is an important characteristic of a dynamic system when it comes to its practical application. This property ensures that the chaotic behavior of the system will not deteriorate or be adversely affected by various factors. There are many methods for creating chaotic systems that are generated by adjusting the corresponding system parameters. However, most of the proposed systems are functions of well-known discrete mappings. In view of this, in this paper we consider a continuous system that illustrates some robust chaos properties.

Ключові слова

robust chaos; Boussinesq-Darcy approximation; 3D Lorenz-like non-autonomous chaotic system; bifurcation diagram; multidimensional recurrence quantification analysis

Повний текст:

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P. Turchin, S. P. Ellner, Living on the edge of chaos: population dynamics of fennoscandian voles, Ecology, 81: 3099-3116, (2000), 3099-3116.

T. R. Young, Chaos and social change: Metaphysics of the postmodern, EcThe Red Feather Institute, USA, (2002), 289-305.

T. Shinbrot, Progress in the control of chaos, Advances in Physics, 44:73-111 (1995), 73-111.

T. Shinbrot, Targeting Chaotic Orbits to the Moon through Recurrence, Physics Letters, A 204 373-378 (1995), 373-378.

Y. Zhao, W. Zhang, H. Su, and J. Yang, Observer-based synchronization of chaotic systems satisfying incremental quadratic constraints and its application in secure communication, IEEE Trans. Syst., Man, Cybern., Syst, (2018), 1-12.

B. R. Brinkley, Managing the centrosome numbers game: from chaos to stability in cancer cell division, Dept of Molecular and Cellular Biology, Baylor College of Medicine, Houston, (2001), 18-21.

S.N.Sarbadhikaria, K.Chakrabarty, Chaos in the brain: a short review alluding to epilepsy, depression, exercise and lateralization, Trends Cell Biol., (2001), 447-457.

J. Barkoulas, N. Travlos, Chaos in an emerging capital market? The case of the Athens Stock Exchange, Applied Financial Economics, 8:3, 231-243 (1998), 231-243.

B. Hasselblatt, A. Katok, A First Course in Dynamics: With a Panorama of Recent Developments, Cambridge University Press, (2003).

E. Zeraoulia, J. C. Sprott, Robust chaos and its applications, World Scientific Publisher, (2011).

M. Majumdar, T. Mitra, Robust ergodic chaos in discounted dynamic optimization models, Economic Theory, 4(1994), 677- 688.

R. Dogaru, A. T. Murgan, S. Ortmann, M. Glesner, Searching for robust chaos in discrete time neural networks using weight space exploration, Int. Conf. Neural Networks, 2(1996), 677- 693.

S. Banerjee, J. A. Yorke, C. Grebogi, Robust chaos, Phys. Rev. Letters, 80(1998), 3049 - 3052.

P. K. Shukla, A. Khare, M. A. Rizvi, S. Stalin, S.Kumar, Applied cryptography using chaos function for fast digital logic-based systems in ubiquitous computing, Entropy, 17(2015), 1387- 1410.

X.Y. Wang, Y. Q. Zhang, X. M. Bao, A colour image encryption scheme using permutation-substitution based on chaos,Entropy, 17(2015), 3877 - 3897.

K. Fallahi, H. Leung, A chaos secure communication scheme based on multiplication modulation, Commun. Nonlinear Sci. Numer. Simulation, 15(2010), 368 - 383.

A. N. Miliou, I. P. Antoniades, S. G. Stavrinides, A. N. Anagnostopoulos, Secure communication by chaotic synchronization: Robustness under noisy conditions, Nonlinear Anal. Real World Applications, 8(2007), 1003 - 1012.

G. Xu, Y.Shekofteh, A. Akgul, C. Li, S. Panahi, A New Chaotic System with a Self-Excited Attractor: Entropy Measurement, Signal Encryption, and Parameter Estimation, Entropy, 20(2018), 86 - 96.

W. San-Um, W. Srichavengsup, A robust hash function using cross-coupled chaotic maps with absolute-valued sinusoidal nonlinearity, Int. J. Adv. Comput. Sci. Applications, 10(2016), 182 - 192.

M. Andrecut, M. Ali, On the occurrence of robust chaos in a smooth system, Mod. Phys. Letters, 15(2001), 391 - 395.

M. Andrecut, M. Ali, Robust chaos in a smooth system, Int. J. Mod. Phys., 15(2001), 177 - 189.

G. Perez, Robust chaos in polynomial unimodal maps, Int. J. Bifurc. Chaos, 14(2004), 2431 - 2437.

Z. Hua, Y. Zhou, Exponential Chaotic Model for Generating Robust Chaos, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 49(2019), 1-12.

K. Allali, Suppression of Chaos in Porous Media Convection under Multifrequency Gravitational Modulation, Advances in Mathematical Physics, 2018(2018), Article ID 1764182, 8 pages.

V. Belozyorov, V. Zaytsev, Recurrence analysis of time series generated by 3D autonomous quadratic dynamical system depending on parameters, Modeling, Dnipropetrovsk University Press, Dnipropetrovsk, 24(2016), 56 –70.

V. Ye. Belozyorov, A novel search method of chaotic autonomous quadratic dynamical systems without equilibrium points, Nonlinear. Dynamics, 86(2016), 835 – 860.

V. Ye. Belozyorov, Reduction method for search of chaotic attractors in generic autonomous quadratic dynamical systems, International Journal of Bifurcation and Chaos, 27(2017), Article ID 1750036, 26 pages.

DOI: http://dx.doi.org/10.15421/141907


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