Period‐doubling route to chaos shows universality

In some systems, as an external parameter is varied, the behavior of the system changes from simple to erratic. For some range of the parameter, the behavior of the system is orderly; for example, it is periodic in time with a period, T. Beyond this range, the behavior does not reproduce itself in T seconds. Instead, two intervals of T are required. In order words, the period doubles to $2T.$ This new periodicity remains over some range of parameter values until another critical value is reached; now a period of $4T$ is required for reproduction. At a certain value of the parameter, an infinite number of doublings has been reached and the behavior has become aperiodic or chaotic. Thus period doubling is a characteristic route for certain systems to follow as they change from simple periodic to complex aperiodic motion.