bifurcation theory

A branch of mathematics concerned with dynamical systems which suffer sudden qualitative changes from an infinitesimal change in a parameter.
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Bifurcation theory — is the mathematical study of changes in the qualitative or topological structure of a given family. Examples of such families are the integral curves of a family of vector fields or, the solutions of a family of differential equations. Most… … Wikipedia
Bifurcation — means the splitting of a main body into two parts.Bifurcation or Bifurcated may refer to:*Bifurcation (law), the division of issues in a trial for example the division of a page into two parts. *Bifurcation theory, the study of bifurcation in… … Wikipedia
Bifurcation diagram — In mathematics, particularly in dynamical systems, a bifurcation diagram shows the possible long term values (equilibria/fixed points or periodic orbits) of a system as a function of a bifurcation parameter in the system. It is usual to represent … Wikipedia
bifurcation — noun /ˌbaɪfəˈkeɪʃən,ˌbaɪfɚˈkeɪʃən/ a) A division into two branches. b) Any place where one thing divides into two. Syn: branching, fork, forking See Also: bifurcate … Wiktionary
Catastrophe theory — This article refers to the study of dynamical systems. For other meanings, see catastrophe. In mathematics, catastrophe theory is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more… … Wikipedia
Chaos theory — This article is about chaos theory in Mathematics. For other uses of Chaos theory, see Chaos Theory (disambiguation). For other uses of Chaos, see Chaos (disambiguation). A plot of the Lorenz attractor for values r = 28, σ = 10, b = 8/3 … Wikipedia
BogdanovTakens bifurcation — In bifurcation theory, a field within mathematics, a Bogdanov Takens bifurcation is a well studied example of a bifurcation with co dimension two, meaning that two parameters must be varied for the bifurcation to occur. It is named after R. I.… … Wikipedia
Hopf bifurcation — In bifurcation theory a Hopf or Andronov Hopf bifurcation is a local bifurcation in which a fixed point ofa dynamical system loses stability as a pair of complex conjugate eigenvalues of the linearization around the fixed point crossthe imaginary … Wikipedia
Pitchfork bifurcation — In bifurcation theory, a field within mathematics, a pitchfork bifurcation is a particular type of local bifurcation. Pitchfork bifurcations, like Hopf bifurcations have two types supercritical or subcritical. In flows, that is, continuous… … Wikipedia
Saddlenode bifurcation — In the mathematical area of bifurcation theory a saddle node bifurcation or tangential bifurcation is a local bifurcation in which two fixed points (or equilibria) of a dynamical system collide and annihilate each other. The term saddle node… … Wikipedia