关键词: 元宇宙, 混沌态, K熵, 股票特征分析

Abstract: The metaverse born in the new era is the intersection of real life and the virtual world. In the real world, media devices are used to provide humans with a virtual binary world. In this binary world, there is no Riemannian space produced by the mass of celestial bodies in the real world, and there is no gravitation and gravity. However, when human consciousness exists in the metaverse, its overall development direction is random, and the information and digital wealth obtained by human consciousness in the metaverse are also common in the real world. Like the real world and the virtual world, the metaverse also has a chaotic effect, full of randomness and regularity. Different from the long evolution and development of the real universe, the construction of the metaverse will go through a process dominated by human awareness of artificial intelligence systems. In this process, the attributes of determinism, randomism, and chaos will accompany the entire life development cycle of the metaverse. In the specific analysis of the chaos of the metaverse, the K-entropy can be used as the characteristic quantity of the degree of unpredictability of the chaotic system. This paper attempts to use it to judge the degree of system chaos in the metaverse development process, and the feasibility of predicting the entire life cycle of the metaverse. Then, the K-entropy analysis of the metaverse's chaotic state verification is applied to the analysis of stock price fluctuation curves, and the specific demonstration is carried out in combination with Keynes' division of different stages of the economic cycle.
At the theoretical stage, this paper reconstructs the M-dimensional phase space of the development index time series during the development process of the metaverse, and conducts correlation calculations based on the distance formula between two points in Euclidean space to derive the maximum likelihood estimation of the metaverse development index K-entropy. At the experimental stage, leveraging Keynes' economic cycle theory, which divides the economic cycle into four stages—recession, depression, recovery, and prosperity—this paper analyzes the segmented characteristics of stock price curves of listed companies in the metaverse cultural media sector in 2021, using publicly available data on the highest and lowest stock price fluctuations. Based on daily stock price trends, the fluctuations in stock prices of listed companies in the metaverse cultural media sector can be roughly divided into four stages: during the prosperity stage, stock prices remain high overall, showing a fluctuating upward trend; during the recession stage, stock prices decline from their peak, exhibiting a fluctuating downward trend; during the depression stage, stock prices remain low overall, displaying a fluctuating downward trend; and during the recovery stage, stock prices rebound from their lowest point, showing a fluctuating upward trend. Simultaneously, K-entropy analysis is performed on the stock price fluctuations of listed companies in the metaverse cultural media sector in two-dimensional Euclidean space, with trading dates as the primary control variable and stock prices as the parameter variable, to obtain a complete “stock price-time” curve for nonlinear analysis. This enables the analysis of stage characteristics of typical stock price fluctuation curves, stage characteristics of atypical stock price fluctuation curves, and entropy analysis of stage characteristics of stock price fluctuation curves. The results show that typical stock price fluctuation curves can exhibit the curve states proposed by Keynes, while atypical stock price fluctuation curves display relatively chaotic states.
As a characteristic quantity for quantifying the unpredictability of chaotic systems, K-entropy reveals the intrinsic dynamical mechanisms of complex systems, demonstrating dual value in the analysis of the metaverse's evolution: it serves both as a quantitative measure of chaos and as a reflection of the interplay between order and disorder in the system. This ability to characterize nonlinear dynamical properties gives it significant advantages in predicting the developmental trajectory of the metaverse. Applying K-entropy to study the characteristics of stock price fluctuation curves, the research conclusions and analytical results mutually corroborate, providing scientific validation and a beneficial supplement to stock price fluctuation curve analysis methods. According to the stage characteristics of stock price fluctuation curves, the segmentation method based on entropy values is an effective approach for quantitative analysis. K-entropy analysis indicates that stock prices with higher K-entropy cannot exhibit clear stage characteristics, displaying disordered development states, while stock prices with lower K-entropy can show distinct stage characteristics, exhibiting relatively ordered development states. The developmental trends of stock price fluctuation curves are consistent with the level of K-entropy.

Key words: metaverse, chaotic state, K-entropy, stock characteristic analysis