Loading [MathJax]/jax/output/CommonHTML/jax.js

Search
This Journal
This Journal
Anywhere
Quick Search in Journals
Enter words / phrases / DOI / ISBN / keywords / authors / etc
Access type:Only show content I have full access toOnly show Open Access
Advanced Search
0 My Cart
Sign in
Institutional Access

System Upgrade on Tue, May 28th, 2024 at 2am (EDT)

Existing users will be able to log into the site and access content. However, E-commerce and registration of new users may not be available for up to 12 hours.
For online purchase, please visit us again. Contact us at customercare@wspc.com for any enquiries.

Tutorials and ReviewsNo Access

COMPLEX DYNAMICS IN MULTISTABLE SYSTEMS

ULRIKE FEUDEL

Theoretical Physics/Complex Systems, ICBM, Carl von Ossietzky University, 26111, Oldenburg, PF 2503, Germany

Search for more papers by this author

https://doi.org/10.1142/S0218127408021233Cited by:200 (Source: Crossref)

Abstract

The coexistence of several stable states for a given set of parameters has been observed in many natural and experimental systems as well as in theoretical models. This paper gives an overview over the wide range of applications in different disciplines of science. Furthermore, different system classes possessing multistability are analyzed in terms of the appearance of coexisting attractors and their basins of attraction. It is shown that multistable systems are very sensitive to perturbations leading to a noise-induced hopping process between attractors. The role of chaotic saddles in the escape from attractors in multistable systems is discussed.

Keywords:

Remember to check out the Most Cited Articles!
Check out our Bifurcation & Chaos

References

R. Aguado and G. Platero, Phys. Rev. Lett. 81, 4971 (1998), DOI: 10.1103/PhysRevLett.81.4971. Crossref, Web of Science, Google Scholar
R. Albert and A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002), DOI: 10.1103/RevModPhys.74.47. Crossref, Web of Science, Google Scholar
F. Arecchiet al., Phys. Rev. Lett. 49, 1217 (1982), DOI: 10.1103/PhysRevLett.49.1217. Crossref, Web of Science, Google Scholar
F. Arecchi, R. Badii and A. Politi, Phys. Rev. A 32, 402 (1985), DOI: 10.1103/PhysRevA.32.402. Crossref, Web of Science, Google Scholar
F. T. Arecchiet al., Phys. Rev. Lett. 65, 2531 (1990), DOI: 10.1103/PhysRevLett.65.2531. Crossref, Web of Science, Google Scholar
M. Arrayáset al., Phys. Rev. Lett. 84, 2556 (2000). Crossref, Web of Science, Google Scholar
V. Astakhovet al., Phys. Rev. E 63, 056212 (2001), DOI: 10.1103/PhysRevE.63.056212. Crossref, Web of Science, Google Scholar
F. Atteneave, Sci. Amer. 225, 62 (1971). Crossref, Web of Science, Google Scholar
J. Baer, J. Opt. Soc. Am. B 3, 1175 (1986), DOI: 10.1364/JOSAB.3.001175. Crossref, Web of Science, Google Scholar
A. Balanov, N. Janson and E. Schöll, Phys. Rev. E 71, 016222 (2005), DOI: 10.1103/PhysRevE.71.016222. Crossref, Web of Science, Google Scholar
M. Baurmann and U. Feudel, Ecol. Compl. 1, 77 (2004), DOI: 10.1016/j.ecocom.2004.01.001. Crossref, Web of Science, Google Scholar
P. Beale, Phys. Rev. A 40, 3998 (1989), DOI: 10.1103/PhysRevA.40.3998. Crossref, Web of Science, Google Scholar
S. Beriet al., Phys. Rev. E 72, 036131 (2005), DOI: 10.1103/PhysRevE.72.036131. Crossref, Web of Science, Google Scholar
B. Bezruchko, M. Prokhorov and Y. Seleznev, Chaos Solit. Fract. 15, 695 (2003), DOI: 10.1016/S0960-0779(02)00171-6. Crossref, Web of Science, Google Scholar
B. Blazejczyk-Okolewska and T. Kapitaniak, Chaos Solit. Fract. 9, 1439 (1998), DOI: 10.1016/S0960-0779(98)00164-7. Crossref, Web of Science, Google Scholar
L. Bonilla, R. Escobedo and G. Dell'Aqua, Phys. Rev. B 73, 115341 (2006), DOI: 10.1103/PhysRevB.73.115341. Crossref, Web of Science, Google Scholar
M. Brambillaet al., Phys. Rev. A 43, 5114 (1991), DOI: 10.1103/PhysRevA.43.5114. Crossref, Web of Science, Google Scholar
M. Brambillaet al., Opt. Commun. 92, 145 (1992), DOI: 10.1016/0030-4018(92)90234-I. Crossref, Web of Science, Google Scholar
V. Brovkinet al., J. Geophys. Res. 103, 31613 (1998), DOI: 10.1029/1998JD200006. Crossref, Web of Science, Google Scholar
C. Canavieret al., J. Neurophysiol. 69, 2252 (1993). Crossref, Web of Science, Google Scholar
R. Carvalho, B. Fernandez and R. V. Mendes, Phys. Lett. A 285, 327 (2001), DOI: 10.1016/S0375-9601(01)00370-X. Crossref, Web of Science, Google Scholar
V. N. Chizhevsky, Phys. Rev. E 64, 036223 (2001), DOI: 10.1103/PhysRevE.64.036223. Crossref, Web of Science, Google Scholar
V. N. Chizhevsky and R. Corbalán, Phys. Rev. E 66, 016201 (2002), DOI: 10.1103/PhysRevE.66.016201. Crossref, Web of Science, Google Scholar
M. de Freitas, R. Viana and C. Grebogi, Nonlin. Dyn. 37, 207 (2004), DOI: 10.1023/B:NODY.0000044645.69344.ac. Crossref, Web of Science, Google Scholar
S. de Souzaet al., Chaos Solit. Fract. 32, 758 (2007). Crossref, Web of Science, Google Scholar
D. Derozier, S. Bielawski and P. Glorieux, Opt. Commun. 83, 97 (1991), DOI: 10.1016/0030-4018(91)90529-M. Crossref, Web of Science, Google Scholar
M. Dykman, Phys. Rev. A 42, 2020 (1990), DOI: 10.1103/PhysRevA.42.2020. Crossref, Web of Science, Google Scholar
M. Dykmanet al., Phys. Rev. Lett. 68, 2718 (1992), DOI: 10.1103/PhysRevLett.68.2718. Crossref, Web of Science, Google Scholar
U. Feudelet al., Phys. Rev. E 54, 71 (1996), DOI: 10.1103/PhysRevE.54.71. Crossref, Web of Science, Google Scholar
U. Feudelet al., Int. J. Bifurcation and Chaos 6, 1319 (1996). Link, Web of Science, Google Scholar
U. Feudel and C. Grebogi, Chaos 7, 597 (1997), DOI: 10.1063/1.166259. Crossref, Web of Science, Google Scholar
U. Feudelet al., Chaos Solit. Fract. 9, 171 (1998), DOI: 10.1016/S0960-0779(97)00058-1. Crossref, Web of Science, Google Scholar
U. Feudelet al., Phys. Rev. E 58, 3060 (1998), DOI: 10.1103/PhysRevE.58.3060. Crossref, Web of Science, Google Scholar
U. Feudel and C. Grebogi, Phys. Rev. Lett. 91, 134102 (2003), DOI: 10.1103/PhysRevLett.91.134102. Crossref, Web of Science, Google Scholar
J. Fosset al., Phys. Rev. Lett. 76, 708 (1996), DOI: 10.1103/PhysRevLett.76.708. Crossref, Web of Science, Google Scholar
J. Foss, F. Moss and J. Milton, Phys. Rev. E 55, 4536 (1997), DOI: 10.1103/PhysRevE.55.4536. Crossref, Web of Science, Google Scholar
J. Foss and J. Milton, J. Neurophysiol. 84, 975 (2000). Crossref, Web of Science, Google Scholar
M. Freidlin and A. Wentzell , Random Perturbations of Dynamical Systems ( Springer-Verlag , Berlin , 1984 ) . Crossref, Google Scholar
S. Gadaleta and G. Dangelmayr, Phys. Rev. E 63, 036217 (2001), DOI: 10.1103/PhysRevE.63.036217. Crossref, Web of Science, Google Scholar
N. Ganapathisubramanian and K. Showalter, J. Chem. Phys. 80, 4177 (1984), DOI: 10.1063/1.447246. Crossref, Web of Science, Google Scholar
B. Goswami, Phys. Rev. E 62, 2068 (2000), DOI: 10.1103/PhysRevE.62.2068. Crossref, Web of Science, Google Scholar
B. Goswami and S. Basu, Phys. Rev. E 65, 036210 (2002), DOI: 10.1103/PhysRevE.65.036210. Crossref, Web of Science, Google Scholar
B. Goswami and S. Basu, Phys. Rev. E 66, 026214 (2002), DOI: 10.1103/PhysRevE.66.026214. Crossref, Web of Science, Google Scholar
B. Goswami, Rivista del Nuovo Cimento 23, 1 (2005). Google Scholar
R. Graham, A. Hamm and T. Tél, Phys. Rev. Lett. 66, 3089 (1991), DOI: 10.1103/PhysRevLett.66.3089. Crossref, Web of Science, Google Scholar
C. Grebogiet al., Phys. Lett. A 99, 415 (1983), DOI: 10.1016/0375-9601(83)90945-3. Crossref, Web of Science, Google Scholar
C. Grebogiet al., Dynamical Systems, Lecture Notes in Mathematics 1342, ed. J. C. Alexander (Springer-Verlag, NY, 1988) pp. 220–250. Crossref, Google Scholar
T. Gross, C. D. D'Lima and B. Blasius, Phys. Rev. Lett. 96, 208701 (2006), DOI: 10.1103/PhysRevLett.96.208701. Crossref, Web of Science, Google Scholar
H. Gutfreund and G. Toulouse , Biology and Computation: A Physicist's Choice ( World Scientific , Singapore , 1994 ) . Link, Google Scholar
P. Hänggi, P. Talkner and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990). Crossref, Web of Science, Google Scholar
J. Hertz , A. Krogh and R. Palmer , Introduction to the Theory of Neural Computation ( Addison-Wesley , NY , 1991 ) . Google Scholar
J. Hirschingeret al., Phys. Lett. A 236, 249 (1997), DOI: 10.1016/S0375-9601(97)00779-2. Crossref, Web of Science, Google Scholar
Hohlet al., Phys. Rev. Lett. 74, 2220 (1996), DOI: 10.1103/PhysRevLett.74.2220. Crossref, Web of Science, Google Scholar
J. Hudson and J. Mankin, J. Chem. Phys. 74, 6171 (1981), DOI: 10.1063/1.441007. Crossref, Web of Science, Google Scholar
J. Huisman and F. Weissing, Nature 402, 407 (1999), DOI: 10.1038/46540. Crossref, Web of Science, Google Scholar
J. Huisman and F. Weissing, Am. Nat. 157, 488 (2001), DOI: 10.1086/319929. Crossref, Web of Science, Google Scholar
K. L. C. Huntet al., J. Chem. Phys. 96, 7019 (1992), DOI: 10.1063/1.462535. Crossref, Web of Science, Google Scholar
K. Ikeda and D. Daido, Phys. Rev. Lett. 46, 474 (1980). Web of Science, Google Scholar
K. Ikeda and K. Kondo, Phys. Rev. Lett. 49, 1467 (1982), DOI: 10.1103/PhysRevLett.49.1467. Crossref, Web of Science, Google Scholar
K. Ikeda and K. Matsumoto, Physica D 29D, 223 (1987). Google Scholar
K. Kaneko, Physica D 41, 137 (1990), DOI: 10.1016/0167-2789(90)90119-A. Crossref, Web of Science, Google Scholar
K. Kaneko (ed.) , Theory and Applications of Coupled Map Lattices ( Wiley , NY , 1993 ) . Google Scholar
K. Kaneko, Phys. Rev. Lett. 78, 2736 (1997), DOI: 10.1103/PhysRevLett.78.2736. Crossref, Web of Science, Google Scholar
K. Kaneko, Physica D 124, 322 (1998), DOI: 10.1016/S0167-2789(98)00205-X. Crossref, Web of Science, Google Scholar
K. Kaneko and I. Tsuda, Chaos 13, 926 (2003), DOI: 10.1063/1.1607783. Crossref, Web of Science, Google Scholar
J. Kastrupet al., Appl. Phys. Lett. 65, 1808 (1994), DOI: 10.1063/1.112850. Crossref, Web of Science, Google Scholar
J. Kennedy and J. A. Yorke, Physica D 51, 213 (1991), DOI: 10.1016/0167-2789(91)90234-Z. Crossref, Web of Science, Google Scholar
S. Kim, S. Park and C. Rye, Phys. Rev. Lett. 78, 1616 (1997), DOI: 10.1103/PhysRevLett.78.1616. Crossref, Web of Science, Google Scholar
W. Knorre, F. Bergter and Z. Simon, Studia Biophysica 49, 81 (1975). Google Scholar
N. Knowlton, Amer. Zool. 32, 674 (1992). Crossref, Google Scholar
H. Kramers, Physica (Utrecht) 7, 284 (1940), DOI: 10.1016/S0031-8914(40)90098-2. Crossref, Google Scholar
B. Krauskopf, Trends in Dynamical Systems, eds. F. Dumortier, D. Roose and A. Vanderbauwhede (Handelingen van de Koninklijke Vlaamse Academie van Belgie, 2006) pp. 33–45. Google Scholar
S. Kraut, U. Feudel and C. Grebogi, Phys. Rev. E 59, 5253 (1999), DOI: 10.1103/PhysRevE.59.5253. Crossref, Web of Science, Google Scholar
S. Kraut and U. Feudel, Phys. Rev. E 66, 015207(R) (2002), DOI: 10.1103/PhysRevE.66.015207. Crossref, Web of Science, Google Scholar
S. Kraut and U. Feudel, Phys. Rev. E 67, 015204(R) (2003), DOI: 10.1103/PhysRevE.67.015204. Crossref, Web of Science, Google Scholar
S. Kraut and U. Feudel, Physica D 181, 222 (2003), DOI: 10.1016/S0167-2789(03)00098-8. Crossref, Web of Science, Google Scholar
S. Kraut and C. Grebogi, Phys. Rev. Lett. 92, 234101 (2004), DOI: 10.1103/PhysRevLett.92.234101. Crossref, Web of Science, Google Scholar
T. Kuhlbrodtet al., Ocean Dyn. 52, 36 (2001). Crossref, Google Scholar
M. V. Kurganskyet al., J. Geophys. Res. (Atmosphere) 101, 4299 (1996), DOI: 10.1029/95JD02703. Crossref, Web of Science, Google Scholar
Y.-C. Lai, Phys. Lett. A 221, 375 (1996), DOI: 10.1016/0375-9601(96)00609-3. Crossref, Web of Science, Google Scholar
Y.-C. Lai and C. Grebogi, Phys. Rev. E 54, 4667 (1996), DOI: 10.1103/PhysRevE.54.4667. Crossref, Web of Science, Google Scholar
R. Lang and K. Kobayashi, IEEE J. Quant. Electron. 16, 347 (1980), DOI: 10.1109/JQE.1980.1070479. Crossref, Web of Science, Google Scholar
J. P. Laplante and T. Erneux, Physica A 188, 89 (1992), DOI: 10.1016/0378-4371(92)90256-P. Crossref, Web of Science, Google Scholar
W. Lauterborn and R. Steinhoff, J. Opt. Soc. Am. B 5, 1097 (1988), DOI: 10.1364/JOSAB.5.001097. Crossref, Web of Science, Google Scholar
G. Lenderink and R. Haarsma, J. Phys. Oceanogr. 24, 1480 (1994). Crossref, Web of Science, Google Scholar
M. A. Lieberman and K. Y. Tsang, Phys. Rev. Lett. 55, 908 (1985), DOI: 10.1103/PhysRevLett.55.908. Crossref, Web of Science, Google Scholar
J. Losson, M. Mackey and A. Longtin, Chaos 3, 167 (1993), DOI: 10.1063/1.165982. Crossref, Google Scholar
D. Luchinsky and P. McClintock, Nature 389, 463 (1997), DOI: 10.1038/38963. Crossref, Web of Science, Google Scholar
D. Luchinskyet al., Int. J. Bifurcation and Chaos 12, 583 (2002). Link, Web of Science, Google Scholar
E. Macau and C. Grebogi, Phys. Rev. E 59, 4062 (1999), DOI: 10.1103/PhysRevE.59.4062. Crossref, Web of Science, Google Scholar
P. Marmillot, M. Kaufman and J.-F. Hervagault, J. Chem. Phys. 95, 1206 (1991), DOI: 10.1063/1.461151. Crossref, Web of Science, Google Scholar
F. Marquardt, J. Harris and S. Girvin, Phys. Rev. Lett. 96, 103901 (2006), DOI: 10.1103/PhysRevLett.96.103901. Crossref, Web of Science, Google Scholar
C. Masoller and N. Abraham, Phys. Rev. A 57, 1313 (1998), DOI: 10.1103/PhysRevA.57.1313. Crossref, Web of Science, Google Scholar
C. Masoller, Phys. Rev. Lett. 88, 034102 (2002), DOI: 10.1103/PhysRevLett.88.034102. Crossref, Web of Science, Google Scholar
B. Martinez-Zerega and A. N. Pisarchik, Phys. Lett. A 340, 212 (2005). Crossref, Web of Science, Google Scholar
R. May, Nature 269, 471 (1977), DOI: 10.1038/269471a0. Crossref, Web of Science, Google Scholar
S. W. McDonaldet al., Physica D 17, 125 (1985), DOI: 10.1016/0167-2789(85)90001-6. Crossref, Web of Science, Google Scholar
C. Miraet al., Int. J. Bifurcation and Chaos 4, 343 (1994). Link, Web of Science, Google Scholar
I. Nagypal and I. Epstein, J. Phys. Chem. 90, 6285 (1986), DOI: 10.1021/j100281a044. Crossref, Web of Science, Google Scholar
M. Orban and I. Epstein, J. Am. Chem. Soc. 104, 5918 (1982), DOI: 10.1021/ja00386a013. Crossref, Web of Science, Google Scholar
M. Orban and I. Epstein, J. Phys. Chem. 86, 3907 (1982), DOI: 10.1021/j100217a003. Crossref, Web of Science, Google Scholar
G. Osipov and M. Sushchik, Phys. Rev. E 58, 7198 (1998), DOI: 10.1103/PhysRevE.58.7198. Crossref, Web of Science, Google Scholar
E. Pampaloniet al., Phys. Rev. Lett. 78, 1042 (1997), DOI: 10.1103/PhysRevLett.78.1042. Crossref, Web of Science, Google Scholar
G. Papsin, A. Hanna and K. Showalter, J. Phys. Chem. 85, 2575 (1981), DOI: 10.1021/j150617a032. Crossref, Web of Science, Google Scholar
A. Pikovsky, O. Popovych and Y. Maistrenko, Phys. Rev. Lett. 87, 044102 (2001), DOI: 10.1103/PhysRevLett.87.044102. Crossref, Web of Science, Google Scholar
A. Pikovsky , M. Rosenblum and J. Kurths , Synchronization ( Cambridge University Press , Cambridge , 2001 ) . Crossref, Google Scholar
A. N. Pisarchik and B. K. Goswami, Phys. Rev. Lett. 84, 1423 (2000), DOI: 10.1103/PhysRevLett.84.1423. Crossref, Web of Science, Google Scholar
A. N. Pisarchik, Phys. Rev. E 64, 046203 (2001), DOI: 10.1103/PhysRevE.64.046203. Crossref, Web of Science, Google Scholar
A. N. Pisarchik and R. Corbalán, Physica D 150, 14 (2001), DOI: 10.1016/S0167-2789(00)00208-6. Crossref, Web of Science, Google Scholar
A. N. Pisarchik, Y. O. Barmenkov and A. V. Kir'yanov, Phys. Rev. E 68, 066211 (2003), DOI: 10.1103/PhysRevE.68.066211. Crossref, Web of Science, Google Scholar
A. N. Pisarchiket al., Phys. Rev. Lett. 96, 244102 (2006), DOI: 10.1103/PhysRevLett.96.244102. Crossref, Web of Science, Google Scholar
L. Poon and C. Grebogi, Phys. Rev. Lett. 75, 4023 (1995), DOI: 10.1103/PhysRevLett.75.4023. Crossref, Web of Science, Google Scholar
S. B. Power and R. Kleeman, J. Phys. Oceanogr. 23, 1670 (1994). Crossref, Web of Science, Google Scholar
F. Prengel, A. Wacker and E. Schöll, Phys. Rev. B 50, 1705 (1994), DOI: 10.1103/PhysRevB.50.1705. Crossref, Web of Science, Google Scholar
K. Pyragas, Phys. Lett. A 170, 421 (1992), DOI: 10.1016/0375-9601(92)90745-8. Crossref, Web of Science, Google Scholar
K. Pyragaset al., Phys. Rev. E 61, 3721 (2000), DOI: 10.1103/PhysRevE.61.3721. Crossref, Web of Science, Google Scholar
S. Rahmstorf, J. Clim. 8, 3028 (1995). Crossref, Web of Science, Google Scholar
P. Rech, M. Beims and J. Gallas, Phys. Rev. E 71, 017202 (2005), DOI: 10.1103/PhysRevE.71.017202. Crossref, Web of Science, Google Scholar
J. Rial Sr.et al., Clim. Change 65, 11 (2004), DOI: 10.1023/B:CLIM.0000037493.89489.3f. Crossref, Web of Science, Google Scholar
A. Roxin, N. Brunel and D. Hansel, Phys. Rev. Lett. 94, 238103 (2005), DOI: 10.1103/PhysRevLett.94.238103. Crossref, Web of Science, Google Scholar
L. A. Safonov and Y. Yamamoto, Phys. Rev. E 73, 031914 (2006), DOI: 10.1103/PhysRevE.73.031914. Crossref, Web of Science, Google Scholar
M. Sainz-Trapágaet al., Phys. Rev. E 70, 031904 (2004). Crossref, Web of Science, Google Scholar
J. M. Saucedo-Solorioet al., J. Opt. Soc. Am. B 20, 490 (2003), DOI: 10.1364/JOSAB.20.000490. Crossref, Web of Science, Google Scholar
M. Schefferet al., Nature 413, 591 (2001), DOI: 10.1038/35098000. Crossref, Web of Science, Google Scholar
G. Schwarz, C. Lehmann and E. Schöll, Phys. Rev. B 61, 10194 (2000), DOI: 10.1103/PhysRevB.61.10194. Crossref, Web of Science, Google Scholar
J. Seoaneet al., Chaos 16, 023101 (2006), DOI: 10.1063/1.2173342. Crossref, Web of Science, Google Scholar
M. Shrimaliet al., Phys. Rev. E 72, 036215 (2005), DOI: 10.1103/PhysRevE.72.036215. Crossref, Web of Science, Google Scholar
M. Shrimaliet al., Int. J. Bifurcation and Chaos 18, 1675 (2008). Link, Web of Science, Google Scholar
R. Simonyi, A. Wolf and H. Swinney, Phys. Rev. Lett. 49, 245 (1982). Crossref, Web of Science, Google Scholar
H. Sun, S. Scott and K. Showalter, Phys. Rev. E 60, 3876 (1999), DOI: 10.1103/PhysRevE.60.3876. Crossref, Web of Science, Google Scholar
M. Timme, F. Wolf and T. Geisel, Phys. Rev. Lett. 89, 154105 (2002), DOI: 10.1103/PhysRevLett.89.154105. Crossref, Web of Science, Google Scholar
T. Vadivasovaet al., Discr. Dyn. Nature Soc. 4, 231 (2000), DOI: 10.1155/S1026022600000224. Crossref, Web of Science, Google Scholar
E. van Nes and M. Scheffer, Ecol. Mod. 159, 117 (2003). Crossref, Web of Science, Google Scholar
J. Wang, P. Sorensen and F. Hymne, J. Chem. Phys. 98, 725 (1994). Crossref, Web of Science, Google Scholar
J. Wanget al., Phys. Chem. Chem. Phys. 5, 5444 (2003), DOI: 10.1039/b310923b. Crossref, Web of Science, Google Scholar
W. Wang, I. Kiss and J. Hudson, Chaos 10, 248 (2000), DOI: 10.1063/1.166470. Crossref, Web of Science, Google Scholar
S. Wieczoreket al., Phys. Rev. E 65, 045207(R) (2002), DOI: 10.1103/PhysRevE.65.045207. Crossref, Web of Science, Google Scholar
F. Willeboordse and K. Kaneko, Phys. Rev. E 72, 026207 (2005), DOI: 10.1103/PhysRevE.72.026207. Crossref, Web of Science, Google Scholar
B. M. Zerega and A. Pisarchik, Phys. Lett. A 340, 212 (2005). Crossref, Web of Science, Google Scholar

Journal cover image

Vol. 18, No. 06

Metrics

Downloaded 392 times

History

Received 1 April 2007

Revised 8 June 2007

Keywords