zbMATH — the first resource for mathematics

Diffusive synchronization of hyperchaotic Lorenz systems. (English) Zbl 1182.37024
Summary: The synchronizing properties of two diffusively coupled hyperchaotic Lorenz 4D systems are investigated by calculating the transverse Lyapunov exponents and by observing the phase space trajectories near the synchronization hyperplane. The effect of parameter mismatch is also observed. A simple electrical circuit described by the Lorenz 4D equations is proposed. Some results from laboratory experiments with two coupled circuits are presented.

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C28 Complex behavior and chaotic systems of ordinary differential equations
Full Text: DOI EuDML
[1] L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Physical Review Letters, vol. 64, no. 8, pp. 821-824, 1990. · Zbl 0938.37019
[2] L. M. Pecora and T. L. Carroll, “Driving systems with chaotic signals,” Physical Review A, vol. 44, no. 4, pp. 2374-2383, 1991.
[3] J. F. Heagy, T. L. Carroll, and L. M. Pecora, “Synchronous chaos in coupled oscillator systems,” Physical Review E, vol. 50, no. 3, pp. 1874-1885, 1994.
[4] L. M. Pecora, T. L. Carroll, G. A. Johnson, D. J. Mar, and J. F. Heagy, “Fundamentals of synchronization in chaotic systems, concepts, and applications,” Chaos, vol. 7, no. 4, pp. 520-543, 1997. · Zbl 0933.37030
[5] K. Pyragas, “Predictable chaos in slightly perturbed unpredictable chaotic systems,” Physics Letters A, vol. 181, no. 3, pp. 203-210, 1993.
[6] J. H. Peng, E. J. Ding, M. Ding, and W. Yang, “Synchronizing hyperchaos with a scalar transmitted signal,” Physical Review Letters, vol. 76, no. 6, pp. 904-907, 1996.
[7] A. Tamasevicious and A. Cenis, “Synchronizing hyperchaos with a single variable,” Physical Review E, vol. 55, no. 1, pp. 297-299, 1997.
[8] A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, “Determining Lyapunov exponents from a time series,” Physica D, vol. 16, no. 3, pp. 285-317, 1985. · Zbl 0585.58037
[9] J. N. Blakely and D. J. Gauthier, “Attractor bubbling in coupled hyperchaotic oscillators,” International Journal of Bifurcation and Chaos, vol. 10, no. 4, pp. 835-847, 2000.
[10] R. Barboza, “Dynamics of a hyperchaotic Lorenz system,” International Journal of Bifurcation and Chaos, vol. 17, no. 12, pp. 4285-4294, 2007. · Zbl 1143.37309
[11] C. Sparrow, The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors, vol. 41 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1982. · Zbl 0504.58001
[12] S. Özo\uguz, A. S. Elwakil, and M. P. Kennedy, “Experimental verification of the butterfly attractor in a modified Lorenz system,” International Journal of Bifurcation and Chaos, vol. 12, no. 7, pp. 1627-1632, 2002.
[13] E. H. Baghious and P. Jarry, ““Lorenz attractor” from differential equations with piecewise-linear terms,” International Journal of Bifurcation and Chaos, vol. 3, no. 1, pp. 201-210, 1993. · Zbl 0873.34045
[14] R. Tokunaga, T. Matsumoto, L. O. Chua, and S. Miyama, “The piecewise-linear Lorenz circuit is chaotic in the sense of Shilnikov,” IEEE Transactions on Circuits and Systems, vol. 37, no. 6, pp. 766-786, 1990. · Zbl 0704.94027
[15] K. M. Cuomo, A. V. Oppenheim, and S. H. Strogatz, “Synchronization of Lorenz-based chaotic circuits with applications to communications,” IEEE Transactions on Circuits and Systems II, vol. 40, no. 10, pp. 626-633, 1993.
[16] R. Barboza, “Experiments on Lorenz system,” in Proceedings of the International Symposium on Nonlinear Theory and Its Applications (NOLTA ’04), vol. 1, pp. 529-532, Fukuoka, Japan, November 2004.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.