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Home > Art, Film & Photography > Bifurcation Theory: Bifurcation Diagram, Catastrophe Theory, Bifurcation Theory, Chaotic Hysteresis, Hopf Bifurcation, Pitchfork Bifurcation
Bifurcation Theory: Bifurcation Diagram, Catastrophe Theory, Bifurcation Theory, Chaotic Hysteresis, Hopf Bifurcation, Pitchfork Bifurcation

Bifurcation Theory: Bifurcation Diagram, Catastrophe Theory, Bifurcation Theory, Chaotic Hysteresis, Hopf Bifurcation, Pitchfork Bifurcation


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Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Bifurcation Diagram, Catastrophe Theory, Bifurcation Theory, Chaotic Hysteresis, Hopf Bifurcation, Pitchfork Bifurcation, Saddle-Node Bifurcation, Period-Doubling Bifurcation, Bogdanov-Takens Bifurcation, Blue Sky Catastrophe, Transcritical Bifurcation, Homoclinic Bifurcation, Heteroclinic Bifurcation, Infinite-Period Bifurcation. Excerpt: 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 stable solutions with a solid line and unstable solutions with a dotted line. Bifurcations in the 1D discrete dynamical systems Logistic map Dynamical systems and List of chaotic maps Bifurcation diagram of the logistic map Animation showing the formation of bifurcation diagram. An example is the bifurcation diagram of the logistic map: The bifurcation parameter r is shown on the horizontal axis of the plot and the vertical axis shows the possible long-term population values of the logistic function. Only the stable solutions are shown here, there are many other unstable solutions which are not shown in this diagram. The bifurcation diagram nicely shows the forking of the possible periods of stable orbits from 1 to 2 to 4 to 8 etc. Each of these bifurcation points is a period-doubling bifurcation . The ratio of the lengths of successive intervals between values of r for which bifurcation occurs converges to the first Feigenbaum constant . r _values=2.5: .001:4; iterations _per _value = 500; output _matrix = zeros(iterations _per _value, length(c _values)); for count = 1: length(c _values) r = r _values(count); y = .5; for i=1:500; y = r*(y*(1-y)); end for i=1: iterations _per _value y = r*(y*(1-y));...


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Product Details
  • ISBN-13: 9781155695877
  • Publisher: Books LLC
  • Publisher Imprint: Books LLC
  • Height: 152 mm
  • Sub Title: Bifurcation Diagram, Catastrophe Theory, Bifurcation Theory, Chaotic Hysteresis, Hopf Bifurcation, Pitchfork Bifurcation
  • Width: 229 mm
  • ISBN-10: 1155695879
  • Publisher Date: 06 May 2010
  • Binding: Paperback
  • Spine Width: 3 mm
  • Weight: 86 gr


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