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Scientists always try their best to record measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors can be random or systematic. Random errors are observed due to the inconsistency or fluctuation in the measurement process, or variations in the quantity itself that is being measured. Such errors fluctuate from being greater than or less than the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a...

Random and Systematic Errors

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Related Experiment Video

Updated: May 11, 2026

Sealable Femtoliter Chamber Arrays for Cell-free Biology

Sealable Femtoliter Chamber Arrays for Cell-free Biology

Published on: March 11, 2015

Stochastic perturbations in open chaotic systems: random versus noisy maps.

Tamás Bódai¹, Eduardo G Altmann, Antonio Endler

¹KlimaCampus, Institute of Meteorology, University of Hamburg, Grindelberg 5, 20144 Hamburg, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|May 18, 2013

Summary

Random perturbations in chaotic systems show that random maps lead to higher escape rates than noisy maps. Escape rates and fractal dimensions in random maps can vary non-monotonically with perturbation intensity.

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Area of Science:

Physics
Nonlinear Dynamics
Statistical Mechanics

Background:

Chaotic systems exhibit sensitive dependence on initial conditions.
Open systems allow trajectories to escape over time.
Random perturbations can alter the dynamics of chaotic systems.

Purpose of the Study:

To compare the effects of independent (white noise) versus simultaneous (random map) perturbations on chaotic open systems.
To analyze the escape rate and fractal dimensions under different perturbation types.
To investigate the accuracy and precision of estimators for these quantities.

Main Methods:

Generalizing the theory of open chaotic systems.
Introducing a time-dependent conditionally-map-invariant measure.
Employing analytical calculations and numerical simulations on area-preserving baker maps.

Main Results:

Random maps consistently yield higher escape rates than noisy maps for equivalent perturbation strengths.
Escape rates and fractal dimensions in random maps can exhibit non-monotonic dependencies on perturbation intensity.
Finite-size estimators for escape rate and fractal dimensions show slow precision improvement with trajectory number and are often biased.

Conclusions:

The type of random perturbation significantly impacts the dynamics of chaotic open systems.
Non-monotonic behaviors in escape rates and fractal dimensions highlight complex responses to perturbations.
Care must be taken when interpreting finite-size estimations due to inherent biases and slow convergence.