Three-cycle, birth

The third-iterate map f (x) is the key to understanding the birth of the period-3 cycle. Any point p in a period-3 cycle repeats every three iterates, by definition, so such points satisfy p = f p) and are therefore fixed points of the third-iterate map. Unfortunately, since / (x) is an eighth-degree polynomial, we cannot solve for the fixed points explicitly. But a graph provides sufficient insight. Figure 10.4.1 plots p (x) for r = 3.835. 

Life cycle is a concept of systems engineering based on the assumption that every product has a finite existence, sealed by three major events initiation (conception), installation (birth) and termination. In between there are two main periods, called here initial development and operation . The last may be divided roughly in immaturity , maturity and decay . The life cycle of a product describes the evolution of its potential from conception to termination (Fig. 1.5). The potential grows continuously to a maximum, after which the decline is inevitable. 

In 1994, nearly one-third of all first births were by women older than 35 years of age, an interesting statistic that highlights the recent trend to delay having children (88,91). With this delay comes an age-related reduction in fertility and the need to employ one or more pharmacological therapies to achieve a live birth. There have been more than 1 million babies born as a result of in vitro fertilization (IVF), with nearly one in three embryo-transfer cycles resulting in a live birth (92). Many infertility treatment options and protocols are available, most of which are highly individualized (Table 46.13) (89). 

Some behaviorists in the nineteenth century suggested that people have cyclical rhythms that influence behavior. People in a number of countries follow this premise and confirm the theory with their own behavior. The theory of biorhythms claims there are three rhythms that originate at birth. The three are physical, emotional and intellectual. They have 23-, 28-, and 33-day cycles, respectively, depicted by sine waves. Each cycle has three phases positive, negative, and transitional. The theory claims that congruence of the periods affects events, moods and actions of a person. One can easily find biorhythm calculators online. Do not confuse biorhythms with biological rhythms, such as circadian rhythm. 

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