Physicists find doubly transient chaos can emerge due to dissipation

November 22, 2013 by Bob Yirka report
Physicists find doubly transient chaos can emerge due to dissipation
Credit: A. E. Motter et al., Phys. Rev. Lett. (2013)

( —A team of researchers, one from the U.S. and the others from Hungary, has found that a condition they've dubbed doubly transient chaos can emerge from a system due to dissipation. In their paper they've had published in the journal Physical Review Letters, the team describes how their experiments with a triple-magnet pendulum showed that even systems that come to stop eventually can have chaos attributes.

At first blush, most people recognize chaos when they see it—a crowd of people, each behaving unpredictably, for example. In physics, chaos can be seen with examples such as the constantly changing images that result from . One property that all chaotic systems have in common is that changes continue occurring (due either to an external force or lack of one such as gravity or friction), aka, transient chaos, as long as the system is in existence—otherwise, the system would dissipate to a non-changing state. But, is that system that results chaotic as well? The researchers in this new effort say yes, but not in the same way as other chaotic systems. For that reason, they have called it doubly transient chaos.

Chaos can exist in even the simplest of systems, such as a pendulum, for example. If it's started and left to swing till it stops, it will follow a routine that can be accurately described mathematically—but not if it is disturbed periodically by an external energy source—say a person reaching over and pushing it a little bit to keep it going. If that extra push can't be described in an orderly way, then the motion and duration of the pendulum's swing can be described as chaotic. The researchers used just such an example to prove their idea about transient chaos. They used a pendulum with three magnets attached to a triangle—suggesting three final states for the pendulum when it finally stops moving. In such a setup, the pendulum was subject to magnetic forces, gravity, and air drag.

In studying the ways in which the swung and eventually stopped, the researchers found that it conformed to doubly transient chaos—one of whose hallmarks is that parameters describing its rate of change to a final state are not constant as they are with transient chaos, but are instead exponential.

The researchers believe that doubly transient may be at play in many other systems (chemical reactions, binary star behavior, etc.) and because of that are likely far less predictable than has been previously thought.

Explore further: Researchers move closer to understanding chaotic motion of a solid body in a fluid

More information: Doubly Transient Chaos: Generic Form of Chaos in Autonomous Dissipative Systems, Phys. Rev. Lett. 111, 194101 (2013)

Chaos is an inherently dynamical phenomenon traditionally studied for trajectories that are either permanently erratic or transiently influenced by permanently erratic ones lying on a set of measure zero. The latter gives rise to the final state sensitivity observed in connection with fractal basin boundaries in conservative scattering systems and driven dissipative systems. Here we focus on the most prevalent case of undriven dissipative systems, whose transient dynamics fall outside the scope of previous studies since no time-dependent solutions can exist for asymptotically long times. We show that such systems can exhibit positive finite-time Lyapunov exponents and fractal-like basin boundaries which nevertheless have codimension one. In sharp contrast to its driven and conservative counterparts, the settling rate to the (fixed-point) attractors grows exponentially in time, meaning that the fraction of trajectories away from the attractors decays superexponentially. While no invariant chaotic sets exist in such cases, the irregular behavior is governed by transient interactions with transient chaotic saddles, which act as effective, time-varying chaotic sets.

Related Stories

Can chaos theory help predict heart attacks?

July 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

September 30, 2013

( —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 cases require ...

Recommended for you

Fusion reactors 'economically viable' say experts

October 2, 2015

Fusion reactors could become an economically viable means of generating electricity within a few decades, and policy makers should start planning to build them as a replacement for conventional nuclear power stations, according ...

Iron-gallium alloy shows promise as a power-generation device

September 29, 2015

An alloy first made nearly two decades ago by the U. S. Navy could provide an efficient new way to produce electricity. The material, dubbed Galfenol, consists of iron doped with the metal gallium. In new experiments, researchers ...

Invisibility cloak might enhance efficiency of solar cells

September 30, 2015

Success of the energy turnaround will depend decisively on the extended use of renewable energy sources. However, their efficiency partly is much smaller than that of conventional energy sources. The efficiency of commercially ...

Extending a battery's lifetime with heat

October 1, 2015

Don't go sticking your electronic devices in a toaster oven just yet, but for a longer-lasting battery, you might someday heat them up when not in use. Over time, the electrodes inside a rechargeable battery cell can grow ...

1 comment

Adjust slider to filter visible comments by rank

Display comments: newest first

not rated yet Nov 23, 2013
Double treble toil and trouble.
Chaos burn and chaos bubble.
Eye of newt and tongue of snake,
Science: magic quack or fake?
They see randomness as law-
Who are slaves to senses raw.

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.