# zbMATH — the first resource for mathematics

New type of intermittency in discontinuous maps. (English) Zbl 0969.37511
Summary: Intermittent behavior originating in a point of discontinuity in 1D maps is investigated. Studying the duration of the laminar phase, we find a logarithmic dependence of the average laminar length $$\langle l\rangle$$ on the control parameter $$\epsilon$$ in contrast to the three conventional types of intermittency characterized by power-law scaling. Analytical considerations give the relation $$\langle l\rangle=\log (\epsilon)/\log(s)+\beta$$ (where $$s$$ is the ‘slope’ at the point of discontinuity). Numerical data obtained from a relaxation oscillator model are in good agreement with these results.

##### MSC:
 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
Full Text:
##### References:
 [1] P. Manneville, Phys. Lett. 75A pp 1– (1979) [2] Y. Pomeau, Commun. Math. Phys. 74 pp 189– (1980) [3] H. G. Schuster, in: Deterministic Chaos (1987) [4] A. Cumming, Phys. Rev. Lett. 59 pp 1633– (1987) [5] P. Alstrom, Phys. Rev. Lett. 61 pp 1679– (1988) [6] P. Alstrom, Phys. Rev. A 40 pp 7239– (1989) [7] P. Alstrom, Phys. Rev. B 41 pp 1308– (1990) [8] B. Christiansen, Phys. Rev. A 42 pp 1891– (1990) [9] R. J. Bagley, Phys. Lett. 114A pp 419– (1986) [10] Da-Ren He, Phys. Lett. A 136 pp 363– (1989) [11] P. C. Bressloff, Phys. Lett. A 150 pp 187– (1990) [12] M. Bauer, Europhys. Lett. 9 pp 191– (1989) [13] D. Barkley, Phys. Rev. Lett. 64 pp 327– (1990) [14] J. Maselko, J. Chem. Phys. 85 pp 6430– (1986) [15] M. Eiswirth, Phys. Rev. Lett. 60 pp 1526– (1988) [16] J. P. Keenep, SIAM J. Appl. Math. 41 pp 503– (1981)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.