34.

[Cover] [Abbreviated Contents] [Contents] [Index]

Page 132

		2.2.2— Attractors

		The coordinates of each point in the phase space correspond to one combination of possible values of the properties that could be measured for a system.

		As time goes by, the values of the properties measured for a chaotic system take on only certain combinations of values. These combination of values correspond to a region in the phase space. This region is called an attractor.

		If we start the system with an unusual set of values of the measured properties that are different from one of these preferred combinations, the values rapidly change to one of these preferred combinations. In the phase space, the unusual starting values correspond to a point away from the attractor. Thus, in the phase space, as time goes by, a point off the attractor rapidly approaches the attractor. That is why it is called an attractor.

		The motion in the phase space before the system reaches the attractor is called the transient behavior. If we analyze the system after this transient behavior has ended, then the phase space set that we find corresponds to the attractor.

		When the fractal dimension of an attractor is not an integer, then the attractor is said to be ''strange."

 

[Cover] [Abbreviated Contents] [Contents] [Index]