Synergetic Phenomena in Active Lattices pp 77-164 | Cite as
Spatial Structures, Wave Fronts, Periodic Waves, Pulses and Solitary Waves in a One-Dimensional Array of Chua’s Circuits
Abstract
Starting with the discovery of deterministic chaos in a 3D dynamical system made by Lorenz in 1963, a great deal of effort was made to build electronic circuits exhibiting chaotic oscillations. At present a large number of such items have been proposed. In particular, special interest has been devoted to the so-called Chua’s circuit (oscillator). Although earlier related proposals existed, this circuit was introduced – in the proper context – by L.O. Chua at the opening lecture given in the Workshop on Nonlinear Theory and its Applications (NOLTA’92), held at Waseda University, Tokyo, in January 1992. Chua’s circuit possesses a large variety of possible dynamical behaviors. By changing the values of control parameters, one can obtain regular behavior or chaotic oscillations. [4.2, 4.6, 4.7]
Keywords
Periodic Orbit Solitary Wave Phase Portrait Slow Motion Chaotic AttractorPreview
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References
- [4.1]Arnéodo, A., Coullet, P. and Tresser, C., “Possible new strange attractors with spiral structure”, Commun. Math. Phys. 79 (1981) 573–579.ADSMATHCrossRefGoogle Scholar
- [4.2]Chua, L. O., CNN: A paradigm for Complexity (World Scientific, Singapore, 1998).MATHGoogle Scholar
- [4.3]Feigenbaum, M. J., “Quantitative Universality for a Class of Nonlinear Transformations”, J. Stat. Phys. 19 (1978) 25–52.MathSciNetADSMATHCrossRefGoogle Scholar
- [4.4]Horn, R. A. and Johnson, C. R., Matrix Analysis (Cambridge University press, Cambridge, 1985).MATHGoogle Scholar
- [4.5]Kazantsev, V. B., Nekorkin, V. I. and Velarde, M. G., “Pulses, fronts and chaotic wave trains in a one-dimensional Chua’s lattice”, Int. J. Bifurcation Chaos 7 (1997) 1775–1790.MathSciNetMATHCrossRefGoogle Scholar
- [4.6]Madan, R. N. (Editor), Chua’s Circuit: A Paradigm for Chaos (World Scientific, Singapore, 1993).MATHGoogle Scholar
- [4.7]Mira, C., “Chua’s circuit and the qualitative theory of dynamical systems”, Int. J. Bifurcation Chaos 7 (1997) 1910–1916.Google Scholar
- [4.8]Nekorkin, V. I. and Chua, L. O., “Spatial disorder and wave fronts in a chain of coupled Chua’s circuits”, Int. J. Bifurcation Chaos 3 (1993) 1281–1291.MathSciNetMATHCrossRefGoogle Scholar
- [4.9]Nekorkin, V. I., Kazantsev, V. B. and Chua, L. O., “Chaotic attractors and waves in a one-dimensional array of modified Chua’s circuits”, Int. J. Bifurcation Chaos 6 (1996) 1295–1317.MathSciNetMATHCrossRefGoogle Scholar
- [4.10]Nekorkin, V. I., Kazantsev, V. B. and Velarde, M. G., “Travelling waves in a circular array of Chua’s circuits”, Int. J. Bifurcation Chaos 6 (1996) 473–484.MATHCrossRefGoogle Scholar
- [4.11]Nekorkin, V. I., Kazantsev, V. B., Rulkov, N. F., Velarde, M. G. and Chua, L. O., “Homoclinic orbits and solitary waves in a one-dimensional array of Chua’s circuits”, I.E.E.E. Trans. Circuits and Systems 42 (1995) 785–801.MathSciNetGoogle Scholar
- [4.12]Shilnikov, L. P., “Chua’s circuit: rigorous results and future problems”, Int. J. Bifurcation Chaos 4 (1994) 489–519.MathSciNetCrossRefGoogle Scholar