Electronic Circuit Simulation of the Lorenz Model With General Circulation

D. C. Saha¹, Anirban Ray² and A. Roy Chowdhury^2,

¹Department of Physics, Prabhu Jagatbandhu College, Andul Howrah, India

²High Energy Physics Division, Department of Physics, Jadavpur University, Kolkata, India

Cite this paper:
D. C. Saha, Anirban Ray and A. Roy Chowdhury. Electronic Circuit Simulation of the Lorenz Model With General Circulation. International Journal of Physics. 2014; 2(5):124-128. doi: 10.12691/ijp-2-5-1

Abstract

The nonlinear dynamics of the Lorenz model of general circulation is investigated with the help of analogue electronic circuits. The structure of the attractor is obtained for the various values of the systems parameters. Existence of two external potential terms in the equation leads to some new and interesting features. The data so generated is collected through the use of NI-6009 USB, analogue to digital converter. This was then used to compute the bifurcation pattern, parametric Lyapunov diagrams, Lyapunov exponents. The system clearly showed a non-periodic doubling route to chaos. This is farther substantiated by the simple variation of Lyapunov exponent in bi-parametric space of forcing parameter for the system. These external forcing is actually very important to settle the various issue arising in the long time behavior.

Keywords:
multistability Shrimps attractor

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References:

[1]	S. H. Strogatz, Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering (Studies in Nonlinearity), 1st Edition, Studies in nonlinearity, Westview Press, 2001.
[2]	T.Matsumoto, A chaotic attractor from chua’s circuit, Circuits and Systems, IEEE Transactions on 31 (12) (1984) 1055-1058.
[3]	L. O. CHUA, Chua’s circuit: An overview ten years later, Journal of Circuits, Systems and Computers 04 (02) (1994) 117-159.
[4]	R. Madan, Chua’s Circuit: A Paradigm for Chaos, Journal of circuits, systems, and computers, World Scientific, 1993.
[5]	T. Carroll, L. M. Pecora, Synchronizing chaotic circuits, Circuits and Systems, IEEE Transactions on 38 (4) (1991) 453-456.
[6]	L. M. Pecora, T. L. Carroll, Driving systems with chaotic signals, Phys. Rev. A 44 (1991) 2374-2383. URL http://link.aps.org/doi/10.1103/PhysRevA.44.2374
[7]	L. M. Pecora, T. L. Carroll, Synchronization in chaotic systems, Phys. Rev. Lett. 64 (1990) 821-824. URL http://link.aps.org/doi/10.1103/PhysRevLett.64.821
[8]	K. Cuomo, A. Oppenheim, S. H. Strogatz, Synchronization of lorenz-based chaotic circuits with applications to communications, Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on 40 (10) (1993) 626-633.
[9]	K. M. Cuomo, A. V. Oppenheim, Circuit implementation of synchronized chaos with applications to communications, Phys. Rev. Lett. 71 (1993) 65-68. URL http://link.aps.org/doi/10.1103/PhysRevLett.71.65
[10]	E. M. Bollt, Review of chaos communication by feedback control of symbolic dynamics, International Journal of Bifurcation and Chaos 13 (02) (2003) 269-285.
[11]	E. S´anchez, M. A. Mat´ıas, Experimental observation of a periodic rotating wave in rings of unidirectionally coupled analog lorenz oscillators, Phys. Rev. E 57 (1998) 6184-6186. URL http://link.aps.org/doi/10.1103/PhysRevE.57.6184
[12]	O. Gonzales, G. Han, J. de Gyvez, E. Sinencio, Lorenz-based chaotic cryptosystem: a monolithic implementation, Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on 47 (8) (2000) 1243-1247.
[13]	E. N. Lorenz, Irregularity: a fundamental property of the atmosphere*, Tellus A 36A (2) (1984) 98-110. URL http://dx.doi.org/10.1111/j.1600-0870.1984.tb00230.x
[14]	H. Broer, C. S. A, R. Vitolo, Bifurcations and strange attractors in the lorenz-84 climate model with seasonal forcing, Nonlinearity 15 (4) (2002) 1205.
[15]	L. van Veen, Baroclinic flow and the lorenz-84 model, International Journal of Bifurcation and Chaos 13 (08) (2003) 2117-2139.
[16]	E. N. Lorenz, Compound windows of the hnon-map, Physica D: Nonlinear Phenomena 237 (13) (2008) 1689-1704. URL http://www.sciencedirect.com/science/article/pii/S0167278907004198.
[17]	J. A. C. Gallas, Structure of the parameter space of the h´enon map, Phys. Rev. Lett. 70 (1993) 2714-2717. URL http://link.aps.org/doi/10.1103/PhysRevLett.70.2714
[18]	C. Masoller, A. Schifino, L. Romanelli, Regular and chaotic behavior in the new lorenz system, Physics Letters A 167 (2) (1992) 185-190.
[19]	C. Masoller, A. S. Schifino, L. Romanelli, Characterization of strange attractors of lorenz model of general circulation of the atmosphere, Chaos, Solitons & Fractals 6 (0) (1995) 357-366, complex Systems in Computational Physics.
[20]	A. Schifino, C. Masoller, Analitical study of the codimension two bifurcations of the new Lorenz system, in: E. Tirapegui,W. Zeller (Eds.), Instabilities and Nonequilibrium Structures V, Vol. 1 of Nonlinear Phenomena and Complex Systems, Springer Netherlands, 1996, pp. 345-348.
[21]	R. Gilmore, M. Lefranc, The Topology of Chaos: Alice in Stretch and Squeezeland, Wiley, 2008. URL http://books.google.co.in/books?id=XuXDrtthXHcC