International Journal of Physics
ISSN (Print): 2333-4568 ISSN (Online): 2333-4576 Website: Editor-in-chief: B.D. Indu
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International Journal of Physics. 2014, 2(6), 217-225
DOI: 10.12691/ijp-2-6-6
Open AccessArticle

Multistability in a Single System with Hidden Attractors- Theory and Experiment

Papri Saha1, Dolonchampa Saha Anirban Ray2 and A. Roy Chowdhury2,

1Department of Physics, B.P. Poddar Institute of Management & Technology, VIP Road, Kolkata, India

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

Pub. Date: November 16, 2014

Cite this paper:
Papri Saha, Dolonchampa Saha Anirban Ray and A. Roy Chowdhury. Multistability in a Single System with Hidden Attractors- Theory and Experiment. International Journal of Physics. 2014; 2(6):217-225. doi: 10.12691/ijp-2-6-6


Existence of more than one attractor for a single nonlinear system and the corresponding generation of multistability is investigated both from the point of view of theory and experiment. The system under consideration is relatively a new one which possess a single stable fixed point but shows many characteristic features of attractors in phase space. It is shown that the change in the initial condition triggers a host of phenomena not observed before in any dynamical system. Change in the initial conditions enables a switch over from one attractor to the other. Our analysis clearly shows the changes in the Poincaré section and the mechanism of formation of unstable periodic orbits. We point out that in spite of these peculiarities, the model does not possess any standard route to bifurcation but one can visualize the change in the periodicity with respect to the parameters and its dependence on the initial conditions. In the next half of our paper we have constructed analogue electric circuit for the equation and have introduced a mechanism for the choice of initial condition with the help of relay in the circuit. These modified circuits were then used to simulate experimentally the sensitivity on the initial conditions and the transition from one to the other attractor.

multistability shrimps attractor

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[1]  M. Brambilla, L. A. Lugiato, and V. Penna. Phys. Rev. A 43, 5114 (1991).
[2]  F. Prengel, A. Wacker, and E. Schöll. Phys. Rev. B 50, 1705 (1994).
[3]  S. Schiff, K. Jerger, D. H. Duong, T. Chang, M. L. Spano, and W. L. Ditto. Nature 370, 615 (1994).
[4]  P. Marmillot, M. Kaufman, and J.-F. Hervagault, J. Chem. Phys. 95, 1206 (1991).
[5]  F. T. Arecchi, R. Meucci, G. Puccioni, and J. Tredicce. Phys. Rev. Lett. 49, 1217 (1982).
[6]  F. T. Arecchi, R. Badii, and A. Politi. Phys. Rev. A 32, 402 (1985).
[7]  H. Sun, S. Scott and K. Showalter. Phys. Rev. E 60, 3876 (1999).
[8]  C. N. Ngonghala, U. Feudel and K. Showalter; Phys. Rev. E 83, 056206 (2011).
[9]  Ulrike Feudel and Celso Grebogi. Chaos 7, 597 (1997).
[10]  A. Balanov, N. Janson, and E. Schöll. Phys. Rev. E 71, 016222 (2005).
[11]  J.C. Sprott, X. Wang. and G. Chrn. Int. J. Bifurc. & Chaos 23, 1350093 (2013)."
[12]  E.N. Lorenz. “Compound windows of the Henon Map”. Physica D 237 (2008)1689.
[13]  J.A.C. Gallas. Structure of the parameter space of the Henon Map; Phys. Rev. Lett.70 (1993) 2714.
[14]  J.C. Sprott. Phys. Rev. E 50(1994) 647.