Bifurcation structure of the nonautonomous quadratic map

Bifurcation structure of the nonautonomous quadratic map

Publication Type:

Journal Article

Authors:

Kapral, R.; Mandel, P.

Source:

Physical Review A, Volume 32, Number 2, p.1076-1081 (1985)

URL:

https://www.scopus.com/inward/record.uri?eid=2-s2.0-0000900558&doi=10.1103%2fPhysRevA.32.1076&partnerID=40&md5=430604458c77746a1d6d7f2e87c14413

Abstract:

The change in the bifurcation structure of a quadratic map due to the introduction of linear time dependence of the bifurcation parameter is investigated. Although nontrivial fixed points do not exist for this system, a bifurcation diagram can be constructed provided the sweep rate is not too large. The characteristic scaling features and hysteresis effects exhibited in this diagram are studied. Since studies of bifurcation points are often carried out by such parameter variations, the results should provide guides for the interpretation of experimental data. © 1985 The American Physical Society.