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S. Drakos and G.N. Pande

. [18] G riffiths D.V., F enton G.A., Seepage beneath water retaining structures founded on spatially random soil , Geotechnique, 1993, 43(4), 577–587. [19] X iu D, K arniadakis G.E., Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos , Computer Methods in Applied Mechanics and Engineering, 2003, 191 (43), 4927–4948 [20] G ray R.M., Toeplitz and Circulant Matrices: A review , Department of electrical Engineering Stanford University, 2006.

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M. Melosik, P. Sniatala and W. Marszalek

R eferences [1] M.E. Yalcin, J.A.K. Suykens, and K. Vandewalle, “True random bit generation from a double-scroll attractor”, IEEE Trans. Circuits and Systems I: Regular Papers 50, 1395–1404 (2004). [2] L. Kocarev and L. Shiguo (Eds.), Chaos-Based Cryptography. Theory, Algorithms and Applications , Springer 2011. [3] K.J. Persohn and R.J Povinelli, “Analyzing logistic map pseudorandom number generators for periodicity inducted by finite precision floatingpoint representation”, Chaos, Solitions and Fractals , 45, 23–244 (2012). [4] P

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Paweł Mitkowski and Wojciech Mitkowski

References Anosov, D. V. (1963). Ergodic properties of geodesic flows on closed Riemanian manifolds of negative curvature, Soviet Mathematics—Doklady   4 : 1153-1156. Arnold, V. I. (1989). Mathematical Methods of Classical Mechanics , 2nd Edn., Springer-Verlag, New York, NY, (translation from Russian). Auslander, J. and Yorke, J. A. (1980). Interval maps, factors of maps and chaos. Tohoku Mathematical Journal. II. Series   32 : 177-188. Bass, J. (1974

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Katarína Janková

] C´ANOVAS, J. S.: Recent results on nonautonomous discrete systems, Bol. Soc. Esp. Mat. Apl. 31 (2010), 33-41. [4] FRANKE, J. E.-SELGRADE, J. F.: Attractors for discrete periodic dynamical systems, J. Math. Anal. Appl. 286 (2003), 64-79. [5] JANKOV´A , K.-SM´I TAL, J.: Maps with random perturbations are generically nonchaotic, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 5 (1995), 1375-1378. [6] JANKOV´A , K.-SM´ITAL, J.: A characterization of chaos, Bull. Austral. Math. Soc. 34 (1986), 283-292. [7

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V.A. Bazhenov, O.S. Pogorelova and T.G. Postnikova

1 Introduction At present chaotic dynamics is one of the most interesting and investigated subjects in nonlinear dynamics. Just deterministic chaos is not an exceptional mode of dynamical systems behaviour; on the contrary, such regimes are observed in many dynamical systems in mathematics, physics, chemistry, biology and medicine. Therefore, the studying of chaotic dynamics is one of the main ways of modern natural science development. Many monographs, papers and textbooks are devoted to chaos studying [ 1 , 2 , 3 , 4 ]. The routes to chaos in

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Dong Yong, Wu Chuansheng and Guo Haimin

., Y. Lin. A Hybrid Particle Swarm Optimization Based on Chaos Strategy to Handle Local Convergence. – Computer Engineering and Applications, Vol. 42 , 2006, No 13, pp. 77-79. 13. Yang, X.-S. Chaos-Enhanced Firefly Algorithm with Automatic Parameter Tuning. – International Journal of Swarm Intelligence Research, Vol. 2 , 2011, pp. 1-11. 14. Lu, Y., X. Liu. A New Population Migration Algorithm Based on the Chaos Theory. – In: Proc. of IEEE 2nd International Symposium on Intelligence Information Processing and Trusted Computing (IPTC), Bangkok, Thailand

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Małgorzata Guzowska

References Bischi, G.I., Gardini, L. (2000). Global Properties of Symmetric Competition Models with Riddling and Blowout Phenomena. Discrete Dynamics in Nature and Society. Vol. 5, 149-160. Day, R.H. (1994). Complex Economic Dynamics. The MIT Press, Cambridge, Massachusetts. Elaydi, S. (1996). An Introduction to Difference Equations. Springer, New York. Elaydi, S. (2008). Discrete Chaos: With Applications in Science and Engineering. Chapman and Hall

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M. Melosik and W. Marszalek

R eferences [1] G. A. Gottwald and I. Melbourne, “A new test for chaos in deterministic systems”, Proc. Royal Soc. London 460, 603–611 (2003). [2] G. A. Gottwald and I. Melbourne, “On the implementation of the 0–1 test for chaos”, SIAM J. Appl. Dyn. Syst. 8, 129–145 (2009). [3] G. A. Gottwald and I. Melbourne, “On the validity of the 0–1 test for chaos”, Nonlinearity 22, 1367–1382 (2009). [4] D Bernardini and G Litak, “An overview of 0–1 test for chaos”, J. Braz. Soc. Mech. Sci. Eng. DOI :10.1007/s40430–015–0453-y (2015). [5

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Rajagopal Karthikeyan and Vaidyanathan Sundarapandian

References [1] ALLIGOOD, K. T.-SAUER, T.-YORKE, J. A. : An Introduction to Dynamical Systems, Springer, New York, USA, 1997. [2] LORENZ, E. N. : Deterministic Nonperiodic Flow, Journal of the Atmospheric Sciences 20 No. 2 (1963), 130-141. [3] LAKSHMANAN, M.-MURALI, K. : Chaos in Nonlinear Oscillators: Controlling and Synchronization, World Scientific, Singapore, 1996.. [4] HAN, S. K.-KERRER, C.-KURAMOTO, Y. : D-Phasing and Bursting in Coupled Neural Oscillators, Physical Review Letters 75 (1995

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Łukasz Korus

References Alsing, P. M., Gavrielides, A. and Kovanis, V. (1994). Using neural networks for controling chaos, Physical Review E   49 (2): 1225-1231. Andrievskii, B. R. and Fradkov, A. L. (2003). Control of chaos: Methods and applications, Automation and Remote Control   64 (5): 673-713. Andrzejak, R. G., Lehnertz, K., Mormann, F., Rieke, C., David, P. and Elger, C. E. (2001). Indications of nonlinear deterministic and finite-dimensional structures in time series of brain