In recent years, nonlinear science has become one of the most active disciplines in the scientific community today. The use of chaos and fractal theory and other nonlinear dynamics principles and methods to study and analyze the functional activity state of the brain has become a new hot spot and frontier in brain science research. The brain is the most functionally and structurally complex organ in the human body, containing hundreds of billions of nerve cells and trillions of neurosynapses. As the basic structural and functional units of the brain, neurons are connected to each other by axons and dendrites, forming a huge and complex neural network. Since each electrode of the EEG reflects the activity of millions of neurons, it contains information about the network hierarchy, especially about the synchronization of local networks and the coupling of networks that are far apart. It is evident that EEG contains a large amount of information about the activity of nonlinear units (structures); it is entirely possible that neural networks formed by huge numbers of neurons and their synapses make EEG signals exhibit chaotic properties. Modern science considers the EEG signal as a nonlinear coupling of a large number of nerve cells, a complex of highly nonlinear multi-unit connections; the EEG activity has deterministic chaotic properties. Currently, common analytical tools in nonlinear dynamics research include: correlation dimension (D2): reflects the dynamical properties of the system and is a parameter describing the information of chaotic degrees of freedom; point correlation dimension (PD2): is more suitable for analysis of finite data than D2, and can track the uncertainty appearing in the data; Lyapunov exponent (L1): describes the sensitivity of chaotic systems to initial values. Kolmogonov entropy (K2): indicates the rate of information loss in chaotic systems, and the reciprocal of K2 reflects the average prediction time; the larger K2 and L1, the less predictable the system is; complexity: in general, it is the complexity of a thing can be measured by the length of the computer language used to describe the thing, and the longer the length of the computer language used to describe the thing, the higher the complexity ; Approximate entropy: is a way to describe the complexity and regularity of a signal, it is a way to quantify the predictability of future values through the knowledge of previous values. These parameters mentioned above are numerically and statistically analyzed from different aspects of the object of the nonlinear dynamical system under study. EEG nonlinear analysis has expanded our understanding of the brain from normal physiological states and different functional states to different pathological states. It has been applied to many research fields such as cognitive function, epilepsy, sleep, dementia, etc. In addition, it has been carried out in neurorehabilitation (e.g., brain injury and compensatory mechanisms, change patterns in different rehabilitation stages, assessment of the degree of impaired consciousness, and prognosis judgment), schizophrenia and depression (abnormal sites and abnormal connections of functional brain activity, etc., are hot spots in psychiatric EEG research), and depth monitoring of anesthesia Extensive research has been conducted. Researchers are expanding the scope of application from diagnosis to treatment (e.g., chaos control may play a role in the prevention and treatment of epilepsy as well as cardiac arrhythmias; the basic principle is to use small perturbations to bring the system into equilibrium under new conditions to suppress seizures and cardiac arrhythmias; chaos control has been successfully implemented in animal tests).