Multi-parametric bifurcations in a piecewise-linear discontinuous map

Avrutin, Viktor ; Schanz, Michael ; Banerjee, Soumitro (2006) Multi-parametric bifurcations in a piecewise-linear discontinuous map Nonlinearity, 19 (8). pp. 1875-1906. ISSN 0951-7715

PDF - Publisher Version

Official URL:

Related URL:


In this paper a one-dimensional piecewise linear map with discontinuous system function is investigated. This map actually represents the normal form of the discrete-time representation of many practical systems in the neighbourhood of the point of discontinuity. In the 3D parameter space of this system we detect an infinite number of co-dimension one bifurcation planes, which meet along an infinite number of co-dimension two bifurcation curves. Furthermore, these curves meet at a few co-dimension three bifurcation points. Therefore, the investigation of the complete structure of the 3D parameter space can be reduced to the investigation of these co-dimension three bifurcations, which turn out to be of a generic type. Tracking the influence of these bifurcations, we explain a broad spectrum of bifurcation scenarios (like period increment and period adding) which are observed under variation of one control parameter. Additionally, the bifurcation structures which are induced by so-called big bang bifurcations and can be observed by variation of two control parameters can be explained.

Item Type:Article
Source:Copyright of this article belongs to Institute of Physics Publishing.
ID Code:21403
Deposited On:20 Nov 2010 12:57
Last Modified:17 May 2016 05:37

Repository Staff Only: item control page