A discrete-time dynamical system with four types of codimension-one bifurcations

L.H.A. Monteiro

Applied Mathematics and Computation, 2019, vol. 354, issue C, 189-191

Abstract: Usually, several discrete-time difference equations are shown in introductory courses on dynamical systems theory, in order to illustrate the occurrence of the most common bifurcations, which are saddle-node, transcritical, pitchfork, and flip. For instance, transcritical and flip bifurcations are found in the well-known logistic map. Here, a first-order difference equation undergoing these four types of bifurcations is presented. The bifurcation diagram is analytically derived and the rationale behind the construction of this equation is explained. The main goal of this didactic work is to give tips on how to write difference equations exhibiting various types of bifurcations, which can be associated with real-world scenarios.

Keywords: Bifurcation; Discrete time; Dynamical system (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300319301389
Full text for ScienceDirect subscribers only

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:apmaco:v:354:y:2019:i:c:p:189-191

DOI: 10.1016/j.amc.2019.02.034

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().