On some properties of nearly conservative dynamics of Ikeda map and its relation with the conservative case

A.P. Kuznetsov, A.V. Savin and D.V. Savin

Physica A: Statistical Mechanics and its Applications, 2008, vol. 387, issue 7, 1464-1474

Abstract: The behavior of the well-known Ikeda map with very weak dissipation (so-called nearly conservative case) is investigated. The changes in the bifurcation structure of the parameter plane while decreasing the dissipation are revealed. It is shown that when the dissipation is very weak the system demonstrates an “intermediate” type of dynamics combining the peculiarities of conservative and dissipative dynamics. The correspondence between the trajectories in the phase space in the conservative case and the transformations of the set of initial conditions in the nearly conservative case has been obtained. The dramatic increase of the number of coexisting low-period attractors and the extraordinary growth of the transient time while the dissipation decreases have been revealed. The method of plotting a bifurcation tree for the set of initial conditions has been used to classify the existing attractors by their structure. Also it was shown that most of the coexisting attractors are destroyed by rather small external noise, and the transient time in noisy driven systems increases still more. The new method of two-parameter analysis for conservative systems was proposed.

Keywords: Multistability; Noise; Chaos; Dissipation (search for similar items in EconPapers)
Date: 2008
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437107011521
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:387:y:2008:i:7:p:1464-1474

DOI: 10.1016/j.physa.2007.10.059

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().