Probing the edge of chaos

Feb 27, 2014

The edge of chaos—right before chaos sets in—is a unique place. It is found in many dynamical systems that cross the boundary between a well-behaved dynamics and a chaotic one. Now, physicists have shown that the distribution—or frequency of occurrence—of the variables constituting the physical characteristics of such systems at the edge of chaos has a very different shape than previously reported distributions. The results, by Miguel Angel Fuentes from the Santa Fe Institute in New Mexico, USA, and Universidad del Desarrollo, Chile, and Alberto Robledo from the National Autonomous University of Mexico, Mexico City, are published in EPJ B. This could help us better understand natural phenomena with a chaotic nature.

In probability theory, the central limit theorem was first developed by an 18th century French mathematician named Abraham de Moivre. It applies to independent random physical quantities or variables, each with a well-defined expected value and well-defined way of varying. This theorem states that once iterated a sufficiently large number of times, these variable physical quantities will be approximately distributed along a central limit—also referred to as the attractor. In chaotic and standard random systems, such distribution is in the shape of a bell curve.

Now, new central limit theorems are emerging for more complex physical processes, such as . In this study, the authors took existing knowledge of the specific position of the attractor at the edge of . To do so, they employed a mathematical formula called the logistic map as a particular example of the dynamic system under study. They found that the distribution of physical properties of such dynamic systems at this specific point at the edge of chaos has a fractal structure not previously known.

Explore further: New insights found in black hole collisions

More information: European Physical Journal B, DOI: 10.1140/epjb/e2014-40882-1

add to favorites email to friend print save as pdf

Related Stories

Can chaos theory help predict heart attacks?

Jul 21, 2010

Chaos models may someday help model cardiac arrhythmias -- abnormal electrical rhythms of the heart, say researchers in the journal CHAOS, which is published by the American Institute of Physics.

New method speeds up stabilisation of chaotic systems

Sep 30, 2013

(Phys.org) —When chaos threatens, speed is essential; for example, when a pacemaker needs to stabilise an irregular heartbeat or a robot has to react to the information received from its environment. Both ...

Recommended for you

New insights found in black hole collisions

6 hours ago

New research provides revelations about the most energetic event in the universe—the merging of two spinning, orbiting black holes into a much larger black hole.

X-rays probe LHC for cause of short circuit

6 hours ago

The LHC has now transitioned from powering tests to the machine checkout phase. This phase involves the full-scale tests of all systems in preparation for beam. Early last Saturday morning, during the ramp-down, ...

Swimming algae offer insights into living fluid dynamics

9 hours ago

None of us would be alive if sperm cells didn't know how to swim, or if the cilia in our lungs couldn't prevent fluid buildup. But we know very little about the dynamics of so-called "living fluids," those ...

Fluctuation X-ray scattering

Mar 26, 2015

In biology, materials science and the energy sciences, structural information provides important insights into the understanding of matter. The link between a structure and its properties can suggest new ...

Hydrodynamics approaches to granular matter

Mar 26, 2015

Sand, rocks, grains, salt or sugar are what physicists call granular media. A better understanding of granular media is important - particularly when mixed with water and air, as it forms the foundations of houses and off-shore ...

User comments : 0

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.