Effects of noise on periodic orbits of the logistic map

• Authors: Feng-guo Li
• Languages of publication: EN

Abstracts

EN

Noise can induce an inverse period-doubling transition and chaos. The effects of noise on each periodic orbit of three different period sequences are investigated for the logistic map. It is found that the dynamical behavior of each orbit, induced by an uncorrelated Gaussian white noise, is different in the mergence transition. For an orbit of the period-six sequence, the maximum of the probability density in the presence of noise is greater than that in the absence of noise. It is also found that, under the same intensity of noise, the effects of uncorrelated Gaussian white noise and exponentially correlated colored (Gaussian) noise on the period-four sequence are different.

Keywords

EN

logistic map; noise; periodic orbits; probability density

Discipline

• 05.40.Ca: Noise
• 05.45.Gg: Control of chaos, applications of chaos

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2008
• Volume: 6
• Issue: 3
• Pages: 539-545

Dates

published

1 - 9 - 2008

online

17 - 7 - 2008

Contributors

author

Feng-guo Li

• School of Physics and Telecommunication Engineering, South China Normal University, 510006, Guangzhou, China

References

• [1] J. Escalona, P. Parmananda, Phys. Rev. E 61, 5987 (2000) http://dx.doi.org/10.1103/PhysRevE.61.5987[Crossref]
• [2] R.R. Hsu, H.T. Su, J.L. Chern, C.C. Chen, Phys. Rev. Lett. 78, 2936 (1997) http://dx.doi.org/10.1103/PhysRevLett.78.2936[Crossref]
• [3] M. Gosak, M. Perc, Phys. Rev. E 76, 037201 (2007) http://dx.doi.org/10.1103/PhysRevE.76.037201[Crossref]
• [4] A. Serletis, A. Shahmoradi, D. Serletis, Chaos Soliton. Fract. 33, 914 (2007) http://dx.doi.org/10.1016/j.chaos.2006.01.046[Crossref]
• [5] A. Serletis, A. Shahmoradi, D. Serletis, Chaos Soliton. Fract. 32, 883 (2007) http://dx.doi.org/10.1016/j.chaos.2005.11.048[Crossref]
• [6] M. Yoshimoto, S. Kurosawa, H. Nagashima, J. Phys. Soc. Jpn. 67, 1924 (1998) http://dx.doi.org/10.1143/JPSJ.67.1924[Crossref]
• [7] K. Matsumoto, I. Tsuda, J. Stat. Phys. 31, 87 (1983) http://dx.doi.org/10.1007/BF01010923[Crossref]
• [8] J.P. Crutchfield, B.A. Huberman, Phys. Lett. 77 A, 407 (1980)
• [9] J.P. Crutchfield, J.D. Farmer, B.A. Huberman, Phys. Rep. 92, 46 (1982) http://dx.doi.org/10.1016/0370-1573(82)90089-8[Crossref]
• [10] J.B. Gao, S.K. Hwang, J.M. Liu, Phys. Rev. Lett. 82, 1132 (1999) http://dx.doi.org/10.1103/PhysRevLett.82.1132[Crossref]
• [11] J.B. Gao, C.C. Chen, S.K. Hwang, J.M. Liu, Int. J. Mod. Phys. B 13, 3283 (1999) http://dx.doi.org/10.1142/S0217979299003027[Crossref]
• [12] S.K. Hwang, J.B. Gao, J.M. Liu, Phys. Rev. E 61, 5162 (2000) http://dx.doi.org/10.1103/PhysRevE.61.5162[Crossref]
• [13] G. Mayer-Kress, H. Haken, J. Stat. Phys. 26, 149 (1981) http://dx.doi.org/10.1007/BF01106791[Crossref]
• [14] J. Perez, C. Jeffries, Phys. Rev. B 26, 3460 (1982) http://dx.doi.org/10.1103/PhysRevB.26.3460[Crossref]
• [15] R.J. Wiener, G.L. Snyder, M.P. Prange, D. Frediani, P.R. Diaz. Phys. Rev. E 55, 5489 (1997) http://dx.doi.org/10.1103/PhysRevE.55.5489[Crossref]
• [16] T.B. Simpson, J.M. Liu, A. Gavrielides, V. Kovanis, P.M. Alsing, Appl. Phys. Lett. 64, 3539 (1994) http://dx.doi.org/10.1063/1.111218[Crossref]

Identifiers

DOI

10.2478/s11534-008-0089-y