Two competing species in super-diffusive dynamical regimes

European Physical Journal B

Volumn 77, Issue 2, 2010, Pages 273-279

  La Cognata, A ^a   Valenti, D ^a   Spagnolo, B ^a   Dubkov, A A ^b  

^a UNIVERSITY OF PALERMO   (Italy)

^b LOBACHEVSKY STATE UNIVERSITY OF NIZHNY NOVGOROD   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

BISTABLE POTENTIAL; DYNAMICAL REGIME; INTERACTION PARAMETERS; LANGEVIN EQUATION; LOTKA-VOLTERRA EQUATIONS; MULTIPLICATIVE NOISE; NOISE SOURCE; STATISTICAL DEPENDENCE; STOCHASTIC RESONANCES; TIME-DEPENDENT INTERACTION;

DIFFERENTIAL EQUATIONS; INTEGRAL EQUATIONS; MAGNETIC RESONANCE;

ACOUSTIC NOISE;

EID: 78149280953     PISSN: 14346028     EISSN: 14346036     Source Type: Journal    
DOI: 10.1140/epjb/e2010-00239-6     Document Type: Article

References (64)

1. L. Brillouin 1949 Am. Sci. 37 554
2. L. von Bertalanffy 1950 Science 111 23 10.1126/science.111.2872.23 1950Sci...111...23V
3. I. Prigogine, G. Nicolis, Self-Organization in Nonequilibrium Systems (John Wiley, New York, 1977)
4. F. Mallamace, H.E. Stanley, The Physics of Complex Systems (New Advances and Perspectives), Proceedings of the Intern School of Physics Enrico Fermi, Course CLX, Società Italiana di Fisica (Bologna, and IOS Press, Amsterdam, 2004)
5. A. Provata I.M. Sokolov B. Spagnolo 2008 Eur. Phys. J. B 65 307 1188.92001 10.1140/epjb/e2008-00380-9 2008EPJB...65..307P
6. A. Provata I.M. Sokolov B. Spagnolo 2008 Eur. Phys. J. B 65 307 1188.92001 10.1140/epjb/e2008-00380-9 2008EPJB...65..307P
7. P. Romanczuk I.D. Couzin L. Schimansky-Geier 2009 Phys. Rev. Lett. 102 010602 10.1103/PhysRevLett.102.010602 2009PhRvL.102a0602R
8. A.N. Kolmogorov 1931 Mathematische Annalen 104 415 0001.14902 10.1007/BF01457949 1512678
9. P. Lévy, Calcul des Probabilités (Gauthier-Villars, Paris, 1925)
10. C.W. Gardiner, Handbook of Stochastic Methods (Springer, Berlin, 2004)
11. L. Arnold W. Horsthemke R. Lefever 1978 Z. Physik B 29 367 10.1007/BF01324036 1978ZPhyB..29..367A
12. J.R. Krebs, N.B. Davies, Behavioural Ecology: An Evolutionary Approach, 4th edn. (Blackwell, Oxford, 1997)
13. D. Tilman, P.M. Kareiva, Spatial Ecology: The Role of Space in Population Dynamic and Interspecific Interactions (Princeton University Press, Princeton, 1997)
14. P. Lévy, Théorie de l'addition des variables aléatoires (Gauthier-Villars, Paris, 1954)
15. B.V. Gnedenko, A.N. Kolmogorov, Limit Distributions for Sums of Random Variables (Addison-Welsey Reading, MA, 1954)
16. G.M. Viswanathan V. Afanasyev S.V. Buldyrev E.J. Murphy P.A. Prince H.E. Stanley 1996 Nature 381 413 10.1038/381413a0 1996Natur.381..413V
17. G.M. Viswanathan S.V. Buldyrev S. Havlin M.G.E. da Luz E.P. Raposo H.E. Stanley 1999 Nature 401 911 10.1038/44831 1999Natur.401..911V
18. A.M. Reynolds 2009 J. Phys. A: Math. Theor. 42 434006 10.1088/1751-8113/42/43/434006 2550515 2009JPhA...42Q4006R
19. F. Bartumeus F. Peters S. Pueyo C. Marrasé J. Catalan 2003 Proc. Natl. Acad. Sci. 100 12771 10.1073/pnas.2137243100 2003PNAS..10012771B
20. A.M. Reynolds 2008 Phys. Rev. E 78 011906 10.1103/PhysRevE.78.011906 2008PhRvE..78a1906R
21. A.M. Reynolds, M.A. Frye, PLoS One 2, e354 (2007)
22. D.W. Sims 2008 Nature 451 1098 10.1038/nature06518 2008Natur.451.1098S
23. A.M. Reynolds A.D. Smith R. Menzel U. Greggers D.R. Reynolds J.R. Riley 2007 Ecology 88 1955 10.1890/06-1916.1
24. J.C. Stout D. Goulson 2001 Anim. Behav. 62 183 10.1006/anbe.2001.1729
25. A.M. Reynolds 2007 Europhys. Lett. 79 30006 10.1209/0295-5075/79/30006 2007EL.....7930006R
26. D. Boyer 2006 Proc. R. Soc. B 273 1743 10.1098/rspb.2005.3462
27. S. Bertrand J.M. Burgos F. Gerlotto J. Atiquipa 2005 J. Mar. Sci. 62 477
28. P. Marchal J.J. Poos F. Quirijns 2007 Fish. Res. 83 33 10.1016/j.fishres.2006.08.025
29. A.M. Edwards 2007 Nature 449 1044 10.1038/nature06199 2007Natur.449.1044E
30. D. Boyer, O. Miramontes, G. Ramos-Fernandez, Evidence for biological Lévy flights stands, e-print arXiv:0802.1762v1 (2007)
31. A.M. Reynolds 2008 Ecology 89 2357 10.1890/07-1688.1
32. M.A. Lomholt K. Tal R. Metzler J. Klafter 2008 Proc. Natl. Acad. Sci. USA. 105 11055 10.1073/pnas.0803117105 2008PNAS..10511055L
33. H.E. Hurst 1951 Trans. Am. Soc. Civ. Eng. 116 770
34. J.A. Viecelli 1998 J. Atmos. Sci. 55 677 10.1175/1520-0469(1998) 055<0677:OTPOSL>2.0.CO;2 1998JAtS...55..677V
35. P.D. Ditlevsen 1999 Geophys. Res. Lett. 26 1441 10.1029/1999GL900252 1999GeoRL..26.1441D
36. W. Feller, An introduction to Probability Theory and Its Apllications (John Wiley and Sons, Inc., New York, 1971), Vol. 2
37. R.N. Mantegna H.E. Stanley 1996 Nature 383 587 10.1038/383587a0 1996Natur.383..587M
38. R.N. Mantegna, H.E. Stanley, An Introduction to Econophysics, Correlations and Complexity in Finance (Cambridge University Press, Cambridge, 2000)
39. R. Metzler J. Klafter 2000 Phys. Rep. 339 1 0984.82032 10.1016/S0370-1573(00)00070-3 1809268 2000PhR...339....1M
40. V.V. Uchaikin 2003 Physics-Uspekhi 46 821 10.1070/PU2003v046n08ABEH001324 2003PhyU...46..821U
41. A.V. Chechkin V. Yu. Gonchar J. Klafter R. Metzler 2006 Adv. Chem. Phys. 133 439
42. B. Dybiec E. Gudowska-Nowak I.M. Sokolov 2007 Phys. Rev. E 76 041122 10.1103/PhysRevE.76.041122 2007PhRvE..76d1122D
43. A.A. Dubkov B. Spagnolo V.V. Uchaikin 2008 Int. J. Bifurcation Chaos Appl. Sci. Eng. 18 2649 1157.82300 10.1142/S0218127408021877 2479323
44. A.A. Dubkov B. Spagnolo 2008 Eur. Phys. J. B 65 361 1188.60028 10.1140/epjb/e2008-00337-0 2452746 2008EPJB...65..361D
45. A.A. Dubkov, A. La Cognata, B. Spagnolo, J. Stat. Mech.: Theory Exp. P01002 (2009)
46. B. Dybiec E. Gudowska-Nowak 2007 New J. Phys. 9 452 10.1088/1367-2630/9/ 12/452 2007NJPh....9..452D
47. B. Dybiec, E. Gudowska-Nowak, J. Stat. Mech.: Theory Exp. P05004 (2009)
48. L. Zhang A. Song J. He 2009 J. Phys. A: Math. Theor. 42 475003 10.1088/1751-8113/42/47/475003 2009JPhA...42U5003Z
49. B. Dybiec 2009 Phys. Rev. E 80 041111 10.1103/PhysRevE.80.041111 2009PhRvE..80d1111D
50. A. Upadhyayaa J.P. Rieub J.A. Glazier Y. Sawadac 2001 Physica A 293 549 10.1016/S0378-4371(01)00009-7 2001PhyA..293..549U
51. J. Bascompte, R. Sole, Modelling Spatiotemporal Dynamics in Ecology (Springer, Berlin, 1998)
52. G. Nicolis, C. Nicolis, Foundations of Complex Systems (World Scientific, Singapore, 2007)
53. D. Valenti A. Fiasconaro B. Spagnolo 2004 Physica A 331 477 10.1016/j.physa.2003.09.036 2044922 2004PhyA..331..477V
54. A.J. Lotka 1920 Proc. Nat. Acad. Sci USA 6 410 10.1073/pnas.6.7.410 1920PNAS....6..410L
55. V. Volterra 1926 Series 6 31
56. A.D. Bazykin, Nonlinear dynamics of interacting populations (World Scientific, Singapore, 1998)
57. J.M.G. Vilar R.V. Solé 1998 Phys. Rev. Lett. 80 4099 10.1103/PhysRevLett.80.4099 1998PhRvL..80.4099V
58. P. Jung P. Hänggi 1991 Phys. Rev. A 44 8032 10.1103/PhysRevA.44.8032 1991PhRvA..44.8032J
59. P. Jung P. Hänggi 1989 Europhys. Lett. 8 505 10.1209/0295-5075/8/6/ 003 1989EL......8..505J
60. L. Gammaitoni P. Hänggi P. Jung F. Marchesoni 1998 Rev. Mod. Phys. 70 223 10.1103/RevModPhys.70.223 1998RvMP...70..223G
61. R.N. Mantegna B. Spagnolo M. Trapanese 2001 Phys. Rev. E 63 011101 10.1103/PhysRevE.63.011101 2001PhRvE..63a1101M
62. P. Talkner 2005 New J. Phys. 7 14 10.1088/1367-2630/7/1/014
63. A. Caruso M.E. Gargano D. Valenti A. Fiasconaro B. Spagnolo 2005 Fluct. Noise Lett. 5 L349 10.1142/S0219477505002768
64. D. Valenti L. Tranchina M. Brai A. Caruso C. Cosentino B. Spagnolo 2008 Ecol. Model. 213 449 10.1016/j.ecolmodel.2008.01.023