Related Experiment Video
Updated: Jun 8, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Origins of Taylor's power law for fluctuation scaling in complex systems
Agata Fronczak1, Piotr Fronczak
1Faculty of Physics, Warsaw University of Technology, PL-00-662 Warsaw, Poland. agatka@if.pw.edu.pl
Abstract:
Taylor's fluctuation scaling (FS) has been observed in many natural and man-made systems revealing an amazing universality of the law. Here, we give a reliable explanation for the origins and abundance of Taylor's FS in different complex systems. The universality of our approach is validated against real world data ranging from bird and insect populations through human chromosomes and traffic intensity in transportation networks to stock market dynamics. Using fundamental principles of statistical physics (both equilibrium and nonequilibrium) we prove that Taylor's law results from the well-defined number of states of a system characterized by the same value of a macroscopic parameter (i.e., the number of birds observed in a given area, traffic intensity measured as a number of cars passing trough a given observation point or daily activity in the stock market measured in millions of dollars).
Related Concept Videos
Taylor Series
Applications of Taylor Series
Convergence of Taylor Series
Real-World Applications of Power Series
Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
The Swing Equation
In a steady-state operation, the mechanical torque (Τm) supplied to the generator is balanced by the electrical torque (Τe)...

