The Logistic Map & Bifurcation
How one simple equation breaks into chaos — the logistic map, the period-doubling route, and Feigenbaum's universal constant 4.669… that appears again and again in nature.
Part of Chaos Theory
22 moments in this segment.
- — The bifurcation diagram. The logistic maps route to chaos — one equation splitting into a fractal fog.
- — Awesome Prime Number Constant (Mills' Constant) - Numberphile. Numberphile
- — What is chaos, by James Yorke. Modesto Montoya
- — Tien-Yien Li. If you find our videos helpful you can support us by buying something from amazon.
- — The mystery of 0.577 - Numberphile. Numberphile
- — The Feigenbaum Constant (4.669) - Numberphile. Numberphile
- — Introduction to Complexity: Period Doubling Route to Chaos Part 2. Complexity Explorer
- — Bifurcation and Chaos: Population Distributions under the Logistic Map. What you're seeing here are probability distributions of a population after 30 years, assuming the population was initially uniformly distributed and the population next year is given by the logistic map:
- — 2.920050977316 - Numberphile. Numberphile
- — Logistic Map Explained (Strogatz Ch. 10): Period-Doubling Route to Chaos | Part 1. Dr. Shane Ross
- — Period-Doubling Route to Chaos & Universality: Feigenbaum Constants in Experiments | Strogatz Ch. 10. Dr. Shane Ross
- — Chaos discrete logistic map. CBlissMath
- — Foundational Concepts In Chaos Theory: An Explanation of Veritasium's Logistic Map Video. In This video I'll go over the foundations of chaos theory to and you'll learn how to prove and predict certain aspects of the Logistic Map.
- — Bifurcation Diagram Live Geogebra Build (as seen on Numberphile). SparksMaths
- — Logistic Map Bifurcation Diagram (An Introduction). Jonathan Mitchell
- — Is the Logistic Map hiding in the Mandelbrot Set? | #SoME3. Desdenova
- — Period 3 Implies Chaos - Dynamical Systems | Lecture 32. In this lecture we learn about one of the most famous results in all of chaos theory: "Period 3 Implies Chaos." This incredible result is due to Li and Yorke and was published in 1975. In fact, it is the first occurrence of the word chaos in the mathematics literature to describe the complex dynamics that can arise in discrete-time dynamical systems. In this lecture we state and prove the "Period 3 Theorem." Interestingly, one needs little more than basic calculus to arrive at the result. Towards the end of the…
- — Explaining the Bifurcation Diagram for the Lorenz Chaotic System. Lazaros Moysis
- — Explaining the Bifurcation Diagram for the Logistic Map. Lazaros Moysis
- — Iterations part 2: period three implies chaos. Mats Vermeeren
- — The Prime Constant - Numberphile. Numberphile
- — ®️ The Mathematics of Sudden Change | Bifurcation Theory Explained. Staiblocks
