๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Hopf bifurcation in a prototype delayed system

โœ Scribed by Chunguang Li; Xiaofeng Liao; Juebang Yu

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
151 KB
Volume
19
Category
Article
ISSN
0960-0779

No coin nor oath required. For personal study only.

โœฆ Synopsis

A simple model described by an autonomous continuous delayed differential equation with one variable, proposed by Uc รŸar, is considered in this paper. We will show that Hopf bifurcations occur in this simple system. The stability of bifurcating periodic solutions and the direction of Hopf bifurcations are determined by applying the normal form theory and the center manifold theorem. Finally, a numerical example is given to demonstrate the effectiveness of the theoretical analysis.

๐Ÿ“œ SIMILAR VOLUMES

Hopf bifurcation in a delayed differenti
Hopf bifurcation in a delayed differentialโ€“algebraic biological economic system
โœ Guodong Zhang; Lulu Zhu; Boshan Chen ๐Ÿ“‚ Article ๐Ÿ“… 2011 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 401 KB

In this paper, we consider a differential-algebraic biological economic system with time delay where the model with Holling type II functional response incorporates a constant prey refuge and prey harvesting. By considering time delay as bifurcation parameter, we analyze the stability and the Hopf b

Hopf bifurcation in multiparty political
Hopf bifurcation in multiparty political systems with time delay in switching
โœ Q.J.A. Khan ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 523 KB

A model of a political system with three political parties and a group of nonaffiliated voters is considered. The model consists of four coupled ordinary differential equations in which members of the third party change allegiance and after a time delay become an active member of one of the other pa