The Chaotic systems are at times described and explained with the help of fractal patterns. A new theory has been developed which uses mathematical means to identify smooth situations with the potential for chaos. An alternative explanation is that, it is that point when a smooth river turns into a chaotic swirl of white water, the tornado which unexpectedly changes courses when the three planets under one another’s gravitational pull interact.
Chaos is a term which everyone is well aware of, and is able to identify. However, the breakthrough in this is that even though we are aware of what chaos is and can identify it, there is not a single mathematical explanation to this term. That is why scientists have tried to come up with a way to mathematically define the chaotic systems.
In July, a paper was published in the journal Chaos, which explains and gives a detail on how the new definition could help identify smooth situations where there could be sighting of chaos, as stated by Brian Hunt the study’s co-author and a mathematician at the University of Maryland, College Park.
Henri Poincare was the first Mathematician to face the wild state while trying to explain the behavior of three celestial bodies under one another’s gravitational zone. Their movements were unpredictable which he termed as “chaos”. However, if someone pays close attention to the pattern it would become easy for him/her to predict it. It is until 1960s, that the scientists noticed the chaos swirling in the universe. At this year the computers started to become powerful enough to crunch numbers and solve equations that could not be solved on paper, said Edward Ott who was an applied physicist at the University of Maryland, College Park.
For example in the case of a simple pendulum, computers have the ability to predict behavior far into the future with the help of few facts. However, some systems were weird, for example, computers needed a lot of pointless extra information just to predict the weather, which is why a 4-hour weather forecast is accurate, where as, a 10-day forecast is a bit more primitive guess.
Hunt and Ott and their team developed a definition of chaos that was shown to be simple and a bit based on quantity similar to entropy. They found that if the expansion entropy is positive the system could become chaotic. On the other hand, zero expansion entropy would not become chaotic.
The new method can help researchers quickly capture the tendency for things to instantly spiral into an abyss of unpredictability. “One thing we’re trying to do is identify when chaos is present but maybe only in rare circumstances,” Hunt said.