to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters)...

In mathematics, particularly in dynamical systems, a bifurcation diagram shows the values visited or approached asymptotically (fixed points, periodic...

In bifurcation theory, a field within mathematics, a pitchfork bifurcation is a particular type of local bifurcation where the system transitions from...

In the mathematical theory of bifurcations, a Hopf bifurcation is a critical point where, as a parameter changes, a system's stability switches and a...

In bifurcation theory, a field within mathematics, a transcritical bifurcation is a particular kind of local bifurcation, meaning that it is characterized...

In the mathematical area of bifurcation theory a saddle-node bifurcation, tangential bifurcation or fold bifurcation is a local bifurcation in which two...

In mathematics, specifically bifurcation theory, the Feigenbaum constants /ˈfaɪɡənˌbaʊm/ δ and α are two mathematical constants which both express ratios...

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 general...

topologically equivalent to the normal form of the bifurcation. For example, the normal form of a saddle-node bifurcation is d x d t = μ + x 2 {\displaystyle {\frac...

constant δ is the limiting ratio of each bifurcation interval to the next between every period-doubling bifurcation. The logistic map is a polynomial mapping...

bifurcations called a Hopf bifurcation and an infinite period bifurcation.[citation needed] Biological applications of bifurcation theory Biophysics Biostatistics...

and often overlaps the lower part of the artery. Behind the angle of bifurcation of the common carotid artery is a reddish-brown oval body known as the...

In bifurcation theory, a field within mathematics, a Bogdanov–Takens bifurcation is a well-studied example of a bifurcation with co-dimension two, meaning...

of a tree are bifurcation ratios, numbers describing how close to balanced a tree is. For each order i in a hierarchy, the ith bifurcation ratio is n i...

chaotic dynamics. Mathematics portal Systems science portal Examples of chaotic systems Advected contours Arnold's cat map Bifurcation theory Bouncing ball...

qualitatively and the dynamical system is said to have gone through a bifurcation. Bifurcation theory considers a structure in phase space (typically a fixed...

increasing rate Hopf bifurcation, in mathematics, a local bifurcation; when the first Lyapunov coefficient is negative, the bifurcation is called supercritical...

A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or...

In mathematics, the irrational numbers (in- + rational) are all the real numbers that are not rational numbers. That is, irrational numbers cannot be...

In dynamical systems theory, a period-doubling bifurcation occurs when a slight change in a system's parameters causes a new periodic trajectory to emerge...

{p}{q}}} is known as a bifurcation: the attracting fixed point "collides" with a repelling period-q cycle. As we pass through the bifurcation parameter into the...

SciSearch) ISI Alerting Services Mathematical Reviews INSPEC Zentralblatt MATH "International Journal of Bifurcation and Chaos in Applied Sciences and...

In mathematics, a critical point is the argument of a function where the function derivative is zero (or undefined, as specified below). The value of...

the bifurcation locus can be thought of as an analog of the Julia set in parameter space. Without doubt, the most famous example of a bifurcation locus...

successive period-doubling bifurcations occur tends to a constant of around 4.6692... He was able to provide a mathematical argument of that fact, and...

Spatial bifurcation is a form of bifurcation theory. The classic bifurcation analysis is referred to as an ordinary differential equation system, which...

systems at local points. Borges anticipated the development of bifurcation theory in mathematics, through "The Garden of Forking Paths" in 1941. In "Garden"...

set theory and mathematical logic. Contents:  Top A B C D E F G H I J K L M N O P Q R S T U V W X Y Z See also References Bifurcation theory the study...

Bifurcation memory is a generalized name for some specific features of the behaviour of the dynamical system near the bifurcation. An example is the recurrent...

In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly...