Monday, February 26, 2024
Companion Links for chaos and logistic map lecture
Logist Map Plots and Analysis by Dirk Brockman for Complexity Explorer
Wolfram demo for the Logistic map and detailed study.
Java Code for Time Series of Logistic Map
GDScript Code for Logistic Map
Andrew Clem ~ Chaos theory contains a very nice explanation of the logistic map and the white bands of periodic behavior inside the chaotic range. Try r=3.84 in the demo used in class, to see a cycle of 3 arise.
See also The birth of period 3, revisited.
Applications of constrained chaos:
Two-dimensional constrained chaos and industrial revolution cycles: "Since the 1760s, at least three industrial revolutions have occurred. To explain this phenomenon, we introduce two-dimensional (2D) constrained chaos. Using a model of innovation dynamics, we show that an industrial-revolution-like technology burst, driven by investment/saving motives for R&D activities, recurs about every one hundred years if the monopolistic use of a new technology lasts about 8 y." Full paper @PNAS.
Non-equilibrium early-warning signals for critical transitions in ecological systems. "We employ landscape-flux theory from nonequilibrium statistical mechanics as a general framework to quantify the global stability of ecological systems and provide warning signals for critical transitions." Full paper @ PNAS.
Wolfram demo for the Logistic map and detailed study.
Java Code for Time Series of Logistic Map
GDScript Code for Logistic Map
Andrew Clem ~ Chaos theory contains a very nice explanation of the logistic map and the white bands of periodic behavior inside the chaotic range. Try r=3.84 in the demo used in class, to see a cycle of 3 arise.
See also The birth of period 3, revisited.
Applications of constrained chaos:
Two-dimensional constrained chaos and industrial revolution cycles: "Since the 1760s, at least three industrial revolutions have occurred. To explain this phenomenon, we introduce two-dimensional (2D) constrained chaos. Using a model of innovation dynamics, we show that an industrial-revolution-like technology burst, driven by investment/saving motives for R&D activities, recurs about every one hundred years if the monopolistic use of a new technology lasts about 8 y." Full paper @PNAS.
Non-equilibrium early-warning signals for critical transitions in ecological systems. "We employ landscape-flux theory from nonequilibrium statistical mechanics as a general framework to quantify the global stability of ecological systems and provide warning signals for critical transitions." Full paper @ PNAS.
Labels: #chaos, #logisticMap
