Gary William Flake - If we increase r [in a logistic map] even more,...

If we increase r [in a logistic map] even more, we will eventually force the system into a period-8 limit cycle, then a period-16 cycle, and so on. The amount that we have to increase r to get another period doubling gets smaller and smaller for each new bifurcation. This cascade of period doublings is reminiscent of the race between Achilles and the tortoise, in that an infinite number of bifurcations (or time steps in the race) can be confined to a local region of finite size. At a very special critical value, the dynamical system will fall into what is essentially an infinite-period limit cycle. This is chaos.

Gary William Flake

They Said So®

Gary William Flake Quotes

;

If we increase r [in a logistic map] even more, we will eventually force the system into a period-8 limit cycle, then a period-16 cycle, and so on. The amount that we have to increase r to get another period doubling gets smaller and smaller for each new bifurcation. This cascade of period doublings is reminiscent of the race between Achilles and the tortoise, in that an infinite number of bifurcations (or time steps in the race) can be confined to a local region of finite size. At a very special critical value, the dynamical system will fall into what is essentially an infinite-period limit cycle. This is chaos. Gary William Flake

They Said So®

Keywords

increase [ logistic map] eventually force system period-8 limit cycle period-16 amount period doubling smaller bifurcation cascade doublings reminiscent race achilles tortoise infinite number bifurcations time steps confined local region finite size special critical dynamical fall essentially infinite-period chaos

Explore other Authors

Pope John Paul II

Tony Campolo

Randall Jarrell

Michael Bay

Walt Whitman

Todd Barry

George Strait

Sam Donaldson

Stephen Ambrose

Buffalo Bill

B. R. Ambedkar

Vanna Bonta

If you are using this quote in any webpage , printmedia or any other places please use the following methods to cite this quotation.

MLA Style Citation

"A quote by Gary William Flake" theysaidso.com, 2024. Apr 26, 2024. https://theysaidso.com/quote/gary-william-flake-if-we-increase-r-in-a-logistic-map-even-more-we-will-eventual

APA Style Citation

"A quote by Gary William Flake" (n.d.). theysaidso.com. Retrieved Apr 26, 2024, from theysaidso.com web site : https://theysaidso.com/quote/gary-william-flake-if-we-increase-r-in-a-logistic-map-even-more-we-will-eventual

Chicago Style Citation

"A quote by Gary William Flake". theysaidso.com, 2024. https://theysaidso.com/quote/gary-william-flake-if-we-increase-r-in-a-logistic-map-even-more-we-will-eventual , accessed Apr 26, 2024.

Comments

Authentication required

You must log in to post a comment.

There are no comments yet.