Stochastic control of attractor preference in a multistable system

Communications in Nonlinear Science and Numerical Simulation

Volumn 17, Issue 11, 2012, Pages 4023-4028

  Martinez Zerega B E ^a,b   Pisarchik, A N ^a  

^a CENTRO DE INVESTIGACIONES EN ÓPTICA   (Mexico)

^b UNIVERSITY OF GUADALAJARA   (Mexico)

Author keywords

Basin of attraction; H non map; Multistability; Noise; Periodic modulation; Probability

Indexed keywords

MODULATION;

BASINS OF ATTRACTION; CO-EXISTING STATE; HÉNON MAP; MULTISTABILITY; MULTISTABLE SYSTEMS; NOISE; NOISE AMPLITUDE; PERIODIC MODULATION; PROBABILISTIC PROPERTIES; STOCHASTIC CONTROL;

STOCHASTIC SYSTEMS;

EID: 84861659160     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2012.03.010     Document Type: Article

References (23)

1. Gammaitoni L., Hänggi P., Jung P., Marchesoni F. Stochastic resonance. Rev Mod Phys 1998, 70:223-287.
2. Pikovsky A.S., Kurths J. Coherence resonance in a noise-driven excitable system. Phys Rev Lett 1997, 78:775-778.
3. Baltanás J.P., López L., Blechman I.I., Landa P.S., Zaikin A., Kurths J., Sanjuán M.A.F. Experimental evidence, numerics, and theory of vibrational resonance in bistable systems. Phys Rev E 2003, 67:066119.
4. Kim S., Park S.H., Ryu C.S. Noise-enchanced multistability in coupled oscillator systems. Phys Rev Lett 1997, 78:1616-1619.
5. Feudel U. Complex dynamics in multistable systems. Int J Bifurcat Chaos 2008, 18:1607-1626.
6. Kaneko K. Dominance of Milnor attractors and noise-induced selection in a multiattractor system. Phys Rev Lett 1997, 78:2736-2739.
7. Kaneko K. On the strength of attractors in a high-dimensional system: Milnor attractor network, robust global attraction, and noise-induced selection. Physica D 1998, 124:322-344.
8. Kraut S., Feudel U., Grebogi C. Preference of attractors in noisy multistable systems. Phys Rev E 1999, 59:5253-5260.
9. Pisarchik A.N. Control of multistability in systems with coexisting attractors. Some Topics of Modern Optics 2008, 326-391. Rinton Press, Paramus.
10. Goswami B.K., Pisarchik A.N. Controlling multistability by small periodic perturbation. Int J Bifurcat Chaos 2008, 18:1645-1673.
11. Masoller C. Noise-induced resonance in delayed feedback systems. Phys Rev Lett 2002, 88:034102.
12. Masoller C. Noise-induced resonance in a semiconductor laser with optical feedback. Physica D 2002, 168-169:171-176.
13. Huerta-Cuellar G., Pisarchik A.N., Barmenkov Yu.O. Experimental characterization of hopping dynamics in a multistable fiber laser. Phys Rev E 2008, 78:035202R.
14. Huerta-Cuellar G., Pisarchik A.N., Kir'yanov A.V., Barmenkov Y.O., del Valle Hernández J. Prebifurcation noise amplification in a fiber laser. Phys Rev E 2009, 79:036204.
15. Hu G., Ditzinger T., Ning C.Z., Haken H. Stochastic resonance without external periodic force. Phys Rev Lett 1993, 71:807-810.
16. Goswami B.K. Controlled destruction of chaos in the multistable regime. Phys Rev E 2007, 76:016219.
17. Goswami B.K., Euzzor S., Al Naimee K., Geltrude A., Meucci R., Arecchi F.T. Control of stochastic multistable systems: experimental demonstration. Phys Rev E 2009, 80:016211.
18. Pisarchik A.N. Controlling the multistability of nonlinear systems with coexisting attractors. Phys Rev E 2001, 64:046203.
19. Pisarchik A.N., Goswami B.K. Annihilation of one of the coexisting attractors in a bistable system. Phys Rev Lett 2000, 84:1423-1426.
20. Pisarchik A.N., Corbalán R. Shift of attractor boundaries in a system with a slow harmonic parameter perturbation. Physica D 2001, 150:14-24.
21. Martínez-Zérega B.E., Pisarchik A.N., Tsimring L. Using periodic modulation to control coexisting attractors induced by delayed feedback. Phys Lett A 2003, 318:102-111.
22. Martínez-Zérega B.E., Pisarchik A.N. Efficiency of the control of coexisting attractors by harmonic modulation applied in different ways. Phys Lett A 2005, 340:212-219.
23. Pisarchik A.N., Jaimes-Reategui R., Sevilla-Escoboza R., Huerta-Cuillar G., Taki M. Rogue waves in a multistable fiber laser. Phys Rev Lett 2011, 107:274101.