Theory of Bifurcations

G. C. Layek ()
Additional contact information
G. C. Layek: The University of Burdwan, Department of Mathematics

Chapter Chapter 6 in An Introduction to Dynamical Systems and Chaos, 2015, pp 203-254 from Springer

Abstract: Abstract Bifurcation means a structural change in the orbit of a system. The bifurcation of a system had been first reported by the French mathematician Henri Poincaré in his work. The study of bifurcation is concerned with how the structural change occurs when the parameter(s) are changing. The structural change and the transition behavior of a system are the central part of dynamical evolution. The point at which bifurcation occurs is known as the bifurcation pointBifurcation point . The behavior of fixed point and the nature of trajectories may change dramatically at bifurcation points. The characters of attractorAttractor and repellorRepellor are altered, in general when bifurcation occurs. The diagram of the parameter values versus the fixed points of the system is known as the bifurcation diagramBifurcation diagram . This chapter deals with important bifurcations of one and two-dimensional systems, their mathematical theories, and some physical applications.

Keywords: Equilibrium Point; Rayleigh Number; Lorenz System; Pitchfork Bifurcation; Stable Node (search for similar items in EconPapers)
Date: 2015
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

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:spr:sprchp:978-81-322-2556-0_6

Ordering information: This item can be ordered from
http://www.springer.com/9788132225560

DOI: 10.1007/978-81-322-2556-0_6

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().