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Chaos in a Noisy World: New Methods and Evidence from Time-Series ...
We also present statistical methods for detecting chaos in time-series data, based on using nonlinear time-series modeling to estimate the Lyapunov exponent λ, which gives the average rate at which perturbation effects grow (λ > 0) or decay (λ < 0).
CHAOS IN A NOISY WORLD: NEW METHODS AND EVIDENCE FROM ... - Peter Turchin
In such borderline cases the fluctuations in short-term Lyapunov exponents may be more informative than the average exponent À for characterizing nonlinear dynamics. Ecologists continue to be intrigued by chaos, the erratic and seemingly unpre- dictable behavior that can result from nonlinearity even in a completely determin- istic system.
Living on the Edge of Chaos: Population Dynamics of Fennoscandian Voles
For the best-fit parameters, the model dynamics are characterized by quasi-chaotic behavior; the global Lyapunov exponent is very close to (and statistically undistinguishable from) zero, but the median local Lyapunov exponent is significantly positive.
War in Ukraine II: The Model - Peter Turchin
More generally, a few studies, I am aware of, that attempted to test the OL model came to the conclusion that the actual exponent relating numerical advantage to war advantage is almost never 2, but is typically between 1 and 2.
Peter Turchin
Peter Turchin is a complexity scientist who works in the field of historical social science that he and his colleagues call: Cliodynamics
America in November 2020: a Structural-Demographic View from Alpha ...
In dynamic systems terms, we are on the cusp with a highly positive Lyapunov exponent. What it means in English is that, unless there is a clean win, we will be in situation where possible trajectories start diverging dramatically. All kinds of outcomes become possible, even ones that seem outlandish right now, such as American Civil War II.
Test "Title" - peterturchin.com
However, both the response (dependent) variable and the pre- dictor (independent)variables are transformedusing the Box-Coxpower transformation (Box and Cox 1964), with the transformationparameter (the exponent) be- ing also estimated from the data.
Table of Contents: Cliodynamics vol. 7 iss. 2 – Peter Turchin
Cliodynamics is a transdisciplinary area of research integrating historical macrosociology, cultural and social evolution, economic history/cliometrics, mathematical modeling of long-term social pr…
Cliodynamica – Peter Turchin
Blog Archive for pre-2025 Posts. For the Current Blog Go to peterturchin.substack.com
Historical Dynamics – Peter Turchin
“An important, original, and timely book―richly detailed and beautifully thought out.” ―Jack A. Goldstone, University of California, Davis “This book is clearly the state of the art in formal modeling and computer simulation of long-term historical changes in territorial states. Elegantly formulated and clearly written, it takes an important topic to a new level of formal ...
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