Chaos

Chaos theory has a variety of applications. One of the most important of these is the stock market. Some researchers believe that they have found non-linear patterns in stock indexes, unemployment patterns, industrial production, and the price changes in Treasury bills. These researchers believe that they can reduce to six or seven the number of variables that determine some stock market trends. However, the researchers concede that if there are non-linear patterns in these financial areas, then anyone acting on those patterns to profit will change the market and introduce new variables which will make the market unpredictable.

Population biology illustrates the deep structure that underlies the apparent confusion in the surface behavior of chaotic systems. Some animal populations exhibit a boom-and-bust pattern in their numbers over a period of years. In some years there is rapid growth in a population of animals, followed by a bust created when the population consumes all of its food supply and most members die from starvation. Soon the few remaining animals have an abundance of food because they have no competition. Since the food resources are so abundant, the few animals multiply rapidly, and some years later, the booming population turns bust again as the food supplies are exhausted from overfeeding. This pattern, however, can only be seen if many data have been gathered over many years. Yet this boom-and-bust pattern has been seen elsewhere, including disease epidemics. Large numbers of people may come down with measles, but in falling ill, they develop antibodies that protect them from future outbreaks. Thus, after years of rising cases of measles, the cases will suddenly decline sharply because so many people are naturally protected by their antibodies. After a period of reduced cases of measles, the outbreaks will rise again and the cycle will start over, unless a program of inoculation is begun.

Chaos theory can also be applied to human biological rhythms. The human body is governed by the rhythmical movements of many dynamical systems: the beating heart, the regular cycle of inhaling and exhaling air that makes up breathing, the circadian rhythm of waking and sleeping, the saccadic (jumping) movements of the eye that allow us to focus and process images in the visual field, the regularities and irregularities in the brain waves of mentally healthy and mentally impaired people as represented on electroencephalograms. None of these dynamic systems is perfect all the time, and when a period of chaotic behavior occurs, it is not necessarily bad. Healthy hearts often exhibit brief chaotic fluctuations, and sick hearts can have regular rhythms. Applying chaos theory to these human dynamic systems provides information about how to reduce sleep disorders, heart disease, and mental disease.