A new chaotic attractor from general Lorenz system family and its electronic experimental implementation

This article introduces a novel three-dimensional continuous autonomous chaotic system with six terms and two quadratic nonlinearities. The new system contains two variational parameters and exhibits Lorenz-like attractors in numerical simulations and experimental measurements. The basic dynamical properties of the new system are analyzed by means of equilibrium points, eigenvalue structures, and Lyapunov exponents. The new system examined in Matlab-Simulink\textregistered and Orcad-PSpice\textregistered. An electronic circuit realization of the proposed system is presented using analog electronic elements such as capacitors, resistors, operational amplifiers and multipliers. The behaviour of the realized system is evaluated with computer simulations.

A new chaotic attractor from general Lorenz system family and its electronic experimental implementation

This article introduces a novel three-dimensional continuous autonomous chaotic system with six terms and two quadratic nonlinearities. The new system contains two variational parameters and exhibits Lorenz-like attractors in numerical simulations and experimental measurements. The basic dynamical properties of the new system are analyzed by means of equilibrium points, eigenvalue structures, and Lyapunov exponents. The new system examined in Matlab-Simulink\textregistered and Orcad-PSpice\textregistered. An electronic circuit realization of the proposed system is presented using analog electronic elements such as capacitors, resistors, operational amplifiers and multipliers. The behaviour of the realized system is evaluated with computer simulations.

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  • G. Chen, X. Dong. From chaos to order: Methodologies, Perspectives and applications; World ScientiŞc, 1998.
  • E.N. Lorenz. “Deterministic nonperiodic flow.”J. Atmos. Sci., Vol. 20, pp. 130–141, 1963.
  • O.E. Rossler. “An equation for continuous chaos.” Physics Letters A, Vol. 57, pp. 397-398, 1976.
  • O.E. Rossler. “Continuous chaos; four prototype equations.” Annals of New York Academy of Science, Vol. 316, pp. 376-392, 1979.
  • J.C. Sprott. “Some simple chaotic flows.” Phys. Rev. E, Vol. 50, pp. R647-R650, 1994.
  • G. Chen, T. Ueta. “Yet another chaotic attractor.” Int. J. Bifurcation and Chaos, Vol. 9, pp. 1465-1466, 1999.
  • T. Ueta, G. Chen.“Bifurcation analysis of Chen’s attractor.” Int. J. Bifurcation and Chaos, Vol 10, No. 8, pp. 1931, 2000. u, T. Zhou, G. Chen, S. Zhang. “The compound structure of Chen’s attractor.” Int. J. Bifurcation and Chaos, Vol. 12, No. 4, pp. 855-858, 2002.
  • A. Vanecek, S. Celikovsky. Control systems: From linear analysis to synthesis of chaos; London: Prentice-Hall, S. Celikovsky, G. Chen. “On a generalized Lorenz canonical form of chaotic systems.” Int. J. Bifurcation and Chaos, Vol. 12, pp. 1789-1812, 2002.
  • J. L¨u, G. Chen. “A new chaotic attractor coined.” Int. J. Bifurcation and Chaos, Vol. 12, No. 3, pp. 659-661, 2002.
  • J. L¨u, G. Chen, S. Zhang. “Dynamical analysis of a new chaotic attractor.” Int. J. Bifurcation and Chaos, Vol. 12, No. 5, pp. 1001-1015, 2002.
  • J. L¨u, G. Chen, D. Cheng, S. Celikovsky. “Bridge the gap between the Lorenz system and the Chen system.” Int. J. Bifurcation and Chaos, Vol. 12, No. 12, pp. 2917-2926, 2002.
  • J. L¨u, G. Chen, D. Cheng. “A new chaotic system and beyond: The generalized Lorenz-like system.” Int. J. Bifurcation and Chaos, Vol. 14, No. 5, pp. 1507-1537, 2004.
  • A. Elwakil, M.P. Kennedy. “Construction of classes of circuit-independent chaotic oscillators using passive-only nonlinear devices.” IEEE Trans. Circ. Syst.-I, Vol. 48, pp. 239–307, 2001.
  • S. ¨Ozo˘guz, A. Elwakil, M.P. Kennedy. “Experimental veriŞcation of the butterfly attractor in a modiŞed Lorenz system.” Int. J. Bifurc. Chaos, Vol. 12, No. 7, pp. 1627–1632, 2002.
  • K.M. Cuomo, A.V. Oppenheim. “Circuit implementation of synchronized chaos with applications to communica- tions.” Physical Review Letters, Vol. 71, pp. 65-68, 1993.
  • S. Nakagawa, T. Saito. “An RC OTA hysteresis chaos generator.” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., Vol. 43, No. 12, pp. 1019–1021, Dec. 1996.
  • J.C. Sprott. “A new class of chaotic circuit.” Physics Letters A, Vol. 266, pp. 19-23, 2000.
  • J.C. Sprott. “Simple chaotic systems and circuits.” Am. J. Physics, Vol. 68, pp. 758-763, 2000.
  • A. Elwakil, M. Kennedy. “Construction of classes of circuit-independent chaotic oscillators using passive-only nonlinear devices.” IEEE Trans. Circuits Syst. I., Vol. 48, pp. 289-307, 2001.
  • S. Yu, J. L¨u, W. Tang, G. Chen. “A general multiscroll Lorenz system family and its realization via digital signal processors.” Chaos, Vol. 16, 033126, 2006.
  • M.E. Yalcin, J.A.K. Suykens, J. Vandewalle, S. Ozoguz. “Families of scroll grid attractors.” Int. J. Bifurcation Chaos, Vol. 12, No. 1, pp. 23-41, 2002.
  • M.E. Yalcin, J.A.K. Suykens, J.P.L Vandewalle. Cellular neural networks, multi-scroll chaos and synchronization. Singapore: World ScientiŞc, 2005.
  • K. S. Tang, G. Q. Zhong, G. Chen, K. F. Man. “Generation of n-scroll attractors via sine function.” IEEE Trans. Circuits Syst., I: Fundam. Theory Appl., Vol. 48, No. 11, pp. 1369-1372, 2001. u, G. Chen. “Generating multiscroll chaotic attractors: Theories, methods and applications.” Int. J. Bifurcation Chaos, Vol. 16, pp. 775-858, 2006.
  • ˙I. Pehlivan, Y. Uyaro˘glu, “Rikitake attractor and its synchronization application for secure communication systems.” Journal of Applied Sciences, Vol. 7, No. 2, pp. 232-236, 2007.
  • ˙I. Pehlivan, Y. Uyaro˘glu. “SimpliŞed chaotic diffusionless Lorenz attractor and its application to secure communi- cation systems”, IET Communications, Vol. 1, No. 5, pp. 1015-1022, 2007.
  • G.Q. Zhong, W. Tang. “Circuitry implementation and synchronization of Chen’s attractor.” Int. J. Bifurcation Chaos, Vol. 12, No. 6, pp. 1423-1427, 2002.
  • K.M. Cuomo, A.V. Oppenheim, S.H. Strogatz. “Synchronization of Lorenz-based chaotic circuits with applications to communications.” IEEE Trans. Circuits and Systems-II: Analog and Digital Signal Processing, Vol. 40, No. 10, pp. 626-633, 1993.