Lorenz-like system design using cellular neural networks

In this study, a Lorenz-like system based on cellular neural networks (CNNs) is proposed. Complex butterflychaotic attractors of Lorenz-like systems are constructed using a three-cell CNN. The proposed system makes the CNNimitate quadratic system dynamics without altering its output nonlinearity. Experimental and numerical analysis resultsare presented in order to verify the convenience of the system.

PDF

___

[1] Sparrow, C. The Lorenz Equations: Bifurcations, Chaos and Strange Attractors. 1st ed. New York, NY, USA: Springer-Verlag, 1982.
[2] Cuomo KM, Oppenheim AV, Strogatz SH. Synchronization of Lorenz-based chaotic circuits with applications to communications. IEEE T Circuits-II 1993; 40: 626-633.
[3] Chen G, Ueta T. Yet another chaotic attractor. Int J Bifurcat Chaos 1999; 9: 1465-1466.
[4] Liu C, Liu T, Liu L, Liu K. A new chaotic attractor. Chaos Soliton Fract 2004; 22: 1031-1038.
[5] Rikitake T. Oscillations of a system of disk dynamos. In: Mathematical Proceedings of the Cambridge Philosophical Society. Cambridge, UK: Cambridge University Press, 1958, pp. 89-105.
[6] Chua L, Yang L. Cellular neural networks: Theory. IEEE T Circuits-II 1988; 35: 732-745.
[7] Chua L. CNN: A paradigm for complexity. In: World Scientific Series on Nonlinear Science. Singapore: World Scientific Publishing, 1988, p. 31.
[8] Chua L, Roska T. The CNN paradigm. IEEE T Circuits-I 1993; 40; 147-156.
[9] Arena P, Baglio S, Fortuna L, Manganaro G. Chua’s circuit can be generated by CNN cells. IEEE T Circuits-I 1995; 42; 123-125.
[10] Manganaro G, Arena P, Fortuna L. Cellular Neural Networks Chaos, Complexity and VLSI Processing. 1st ed. Berlin, Germany: Springer, 1999.
[11] Caponetto R, Lavorgna M, Occhipinti L. Cellular neural networks in secure transmission applications. In: CNNA’96; 24–26 June 1996; Seville, Spain. New York, NY, USA: IEEE. pp. 411-416.
[12] Günay E. MLC circuit in the frame of CNN. Int J Bifurcat Chaos 2010; 20: 3267-3274.
[13] Rössler OE. An equation for continuous chaos. Phy Lett A 1976; 57: 397-398.
[14] Arena P, Fortuna L, Rizzo A, Xibilia MG. Extending the CNN paradigm to approximate chaotic systems with multivariable nonlinearities. In: ISCAS 2000; 28–31 May 2000; Geneva, Switzerland. New York, NY, USA: IEEE. pp. 141-144.
[15] Lorenz EN. Deterministic nonperiodic flow. J Atmos Sci 1963; 20: 130-141.