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Topic: Bifurcation

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In the News (Fri 19 Jul 19)

  Bifurcation diagram for quadratic maps
There is a good way to trace bifurcations of period of attracting orbit on the (x, c) plane by the bifurcation diagram of f (it is very similar to the "logistic bifurcation map").
At the lower part of the bifurcation diagram you see chaotic bands and white narrow holes of windows of periodic dynamics.
Bifurcation map (the right picture) compliments the "spider" and shows its interior.
www.ibiblio.org /e-notes/MSet/Logis.htm   (377 words)

  PlanetMath: bifurcation
For example, the branching of the Feigenbaum tree is an instance of bifurcation.
A cascade of bifurcations is a precursor to chaos.
This is version 3 of bifurcation, born on 2002-04-07, modified 2004-02-25.
planetmath.org /encyclopedia/Bifurcation.html   (92 words)

Bifurcation arises perhaps most often in family law cases, in which the question of whether or not to grant a divorce is considered independently of the distribution of assets and children.
Judges in different states and circuits have expressed different levels of willingness to bifurcate cases; indeed, a bifurcation is generally viewed as a tip for the defendant, but this does not imply that bifurcation is not necessary or appropriate protect parties who the law does not recognize as legally liable.
Thus, bifurcation is proper where liability is based on hotly disputed facts and there are complex damages issues including whether certain injuries were caused by the accident or were the natural result of degeneration, all of which would require a tremendous amount of the trial court's time and expense.
members.tripod.com /trilliondollar/bifurcation.html   (835 words)

 WOB Tutorial 4
Depending on the type of bifurcation, a new branch may bifurcate off distinct from the branch that was calculated during the continuation.
Since bifurcation is frequently tied to symmetry, or to symmetry breaking, it is natural to exploit symmetry also for computational purposes.
Since numerical bifurcation has reached a level of some sophistication, it may be attempted to give a weighting review of some of the past research.
www.bifurcation.de /tutor/tutor4/tutor4.html   (2899 words)

 Local Bifurcation Theory: Impact Oscillators
Based on the general discussion of bifurcation theory and stability analysis, we will classify various kinds of smooth local bifurcations of codimension-1 that our system model shows as one of the system parameters is changed.
For the case of pitchfork (symmetry breaking) bifurcation phase plane projection of the two asymmetric orbits and tracking of unstable symmetric orbit was necessary to establish the nature of the bifurcation.
The fact that it is a pitchfork bifurcation was established by observing the phase plane projection of the two asymmetric orbits in the vicinity of the bifurcation point.
chaos4.phy.ohiou.edu /~thomas/chaos/impact-sm-bifur.html   (996 words)

 Bifurcation Diagram   (Site not responding. Last check: )
For all these reasons, a bifurcation diagram  is a particularly powerful method for studying the attractors in the quadratic map.
Recall that a bifurcation diagram is a plot of an asymptotic solution on the vertical axis and a control parameter on the horizontal axis.
Much of the structure in the bifurcation diagram can only be understood by keeping track of both the stable attracting solutions and the unstable repelling solutions, as we did in constructing the orbit stability diagram (Figure 2.13).
cnls.lanl.gov /People/nbt/Book/node39.html   (666 words)

 CaliforniaDivorce.com, California Divorce; Bifurcation
In both of those situations, the court will order that the trial is to be “bifurcated.” This means either that the marital status is terminated and the parties are restored to their single status or a separate trial is to be held concerning a specific issue.
Initially, the party requesting bifurcation must serve his or her preliminary declaration of disclosure on the other spouse before the request for bifurcation is filed.
To be assured that the clerk places a bifurcation motion on the court’s calendar before the end of the year, the motion should be filed not later than November 15th.
www.californiadivorce.com /articles/bifurcationbody.htm   (899 words)

 Lien Stripping or Bifurcation
Under the bankruptcy code, a lien, other than a lien secured solely by a personal residence, is deemed secured only to the extent of the value of the property, at the time of the bankruptcy filing.
The real value of bifurcation is that John, in all likelihood, will only have to pay back $20,000 of the loan, as unsecured debts are typically discharged in bankruptcy.
When bifurcation is applied, the choice will be to pay back the secured portion in one lump sum in a Chapter 7 bankruptcy, or over three to five years in a Chapter 13 bankruptcy.
www.uschamber.com /sb/business/P12/P12_1355.asp   (701 words)

 Bifurcation theory - Wikipedia, the free encyclopedia
In mathematics, specifically in the study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in the system's long-term dynamical behaviour.
Infinite-period bifurcation in which a stable node and saddle point simultaneously occur on a limit cycle.
The codimension of a bifurcation is the number of parameters which must be varied for the bifurcation to occur.
en.wikipedia.org /wiki/Bifurcation_theory   (611 words)

 Bifurcation analysis of continuous time dynamics of oscillatory neural networks
In spite of the fact that bifurcation analysis is applied to a wide variety of systems, problems ranging from engineering chemical reactions to systems in surface and solid state physics (Krischer, 1990) and Hamiltonian mechanics (Abraham and Marsden, 1978), only a few bifurcation analyses have been performed for neural networks (Khiblik, Borisyuk, 1992).
Bifurcation diagram for equation (3), only two Hopf bifurcations are shown; note the folded form of the upper one.
Bifurcation diagram for equation (3) in this case P is fixed and Kmg = -Kg, and Kmm = -Kgg are varied and the Hopf bifurcation curve is traced out.
sulcus.berkeley.edu /FreemanWWW/manuscripts/ID8/93.html   (5526 words)

 Bifurcation pieces
Bifurcation pieces is a class of pieces that employs movement in two legs of arbitrary length.
There are four ways in which a bifurcation piece interacts with another piece to enter the second leg of the move.
Bifurcation pieces are further differentiated with respect to their capture and movement capability.
hem.passagen.se /melki9/bifurcation.htm   (573 words)

 Algorithms for Molecular Biology | Full text | Inverse bifurcation analysis: application to simple gene systems
For instance, mathematical and symbolic bifurcation analysis has led to an understanding of the possible dynamical behaviors that may arise out of simple gene systems (for a monograph, see [2], examples of more recent papers dealing with natural, designed, and model systems are [3-7]).
For cell cycle models, bifurcation diagrams have given biologists a systems-level perspective of the roles played by the various constituent modules, as well as providing the ability to predict the behavior of mutant cells [8,9].
The notion of "inverse bifurcation" was first introduced into biology in [13]; more recently, another inverse bifurcation problem from mathematical ecology was studied in [14] by integral equation methods.
www.almob.org /content/1/1/11   (4468 words)

 Bifurcation - Wikipedia, the free encyclopedia
A bifurcation can be a qualitative change of the attractor of a dynamical system as the result of a moving parameter.
Clothing may be bifurcated, as in trousers or pants, or unbifurcated, as in a skirt, kilt, robe, or dress.
A bifurcation is a logical fallacy of false dilemma.
en.wikipedia.org /wiki/Bifurcation   (410 words)

bifurcation is a place or point of branching or forking into qualitatively new types of behavior.
A typical bifurcation map is shown in Figure 1.
The number of the primary bifurcations of the psyche, caused by the archetypes as attractors, are limited in number for each of us.
www.schuelers.com /ChaosPsyche/part_1_7.htm   (362 words)

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