1 / 4

Critical Scaling Behavior near The Accumulation Point

Critical Scaling Behavior near The Accumulation Point. Eui-Sun Lee Department of Physics Kangwon National University. The transition to chaos through an infinite sequence of period-double bifurcation occurs at the accumulation point A ∞. Bifurcation diagram. Parameter Scaling Factor.

Download Presentation

Critical Scaling Behavior near The Accumulation Point

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Critical Scaling Behavior near The Accumulation Point • Eui-Sun Lee • Department of Physics • Kangwon National University The transition to chaos through an infinite sequence of period-double bifurcation occurs at the accumulation point A∞ . Bifurcation diagram

  2. Parameter Scaling Factor Follow the period–doubling bifurcation pointAn of the period – 2n orbit (n=0,1,2,3…) with the stability multiplierλn= -1. An converges to its accumulation point A∞ geometrically with ratio 1/ δ , Define the parameter scaling factor of the level n, as n → ∞ . Converges to and = 4.6692… .

  3. Orbit Scaling Factor Find a period–2n orbit point x n with the maximum distance at A n . converges to its origin point x = 0 geometrically with ratio 1/ α , Define the orbital scaling factor of the level n, and Converges to as n → ∞ . = - 2.5029… .

  4. Parameter and Orbital Scaling Factor Parameter Scaling Factor Orbital Scaling Factor

More Related