[A biomathematical model of human operator's falling asleep]

Sleep, an essential biological state, involves significant reductions in physical activity, sensory awareness, and interaction with the environment. This complex physiological process is primarily regulated by specific brain regions, notably the hypothalamus and pons, which govern the sleep-wake cycle or circadian rhythm.
The circadian rhythm, a nearly 24-hour cycle, is deeply influenced by environmental light cues. Light exposure directly affects the hypothalamus, which in turn regulates...

Sleep is an essential physiological process vital to maintaining overall well-being. The reticular activating system (RAS), a network of neurons in the brainstem, regulates wakefulness and sleep. While it may seem passive, sleep consists of distinct cycles, each with its unique characteristics and functions. Two key sleep phases are non-rapid eye movement (NREM) and  rapid eye movement (REM).
NREM Sleep
NREM sleep comprises four progressive stages that seamlessly merge:

Sleep progresses through distinct stages, each characterized by specific brain wave patterns and physiological responses ranging from wakefulness to stages of non-rapid eye movement, known as non-REM, to rapid eye movement, referred to as REM. Understanding these stages helps in recognizing how sleep supports various bodily and cognitive functions.
Before sleep begins, in wakefulness, the brain exhibits primarily beta waves, which are high in frequency and low in amplitude, indicating alertness...

The optimal arousal theory suggests that performance is maximized when an individual experiences a moderate level of arousal. This theory is closely tied to the Yerkes-Dodson law, which illustrates an inverted U-shaped relationship between arousal and performance. The law, formulated by psychologists Robert Yerkes and John Dodson, implies an ideal arousal level for optimal performance, and deviations from this level can lead to declines in effectiveness.
Inverted U-Shaped Performance Curve
The...

The sleep cycle, an integral part of human health, consists of several stages with distinct characteristics and functions. It begins with a transition from wakefulness to sleep, known as the light sleep phase, followed by the restorative deep sleep phase, essential for physical recovery and growth. The cycle concludes with the Rapid Eye Movement (REM) phase, characterized by high brain activity and vivid dreaming. Insomnia, a prevalent sleep disorder, involves difficulty falling asleep, staying...

Somnambulism, commonly known as sleepwalking, involves individuals engaging in activities ranging from simple walking to more complex behaviors such as driving. Sleepwalking typically occurs during the slow-wave sleep stages 3 and 4 early in the night when the person is not dreaming, contradicting the myth that sleepwalkers are acting out their dreams.
Factors that increase the likelihood of sleepwalking include sleep deprivation and alcohol consumption. Contrary to common beliefs, it is safe...