Dynamical Behavior and Analysis for Diverse Models in the Complex Systems

Abstract

Application of ideas from fractal and chaos theories to characterize rainfall is one of the most active and exciting areas of research. Many studies performed thus far have yielded evidence of the existence of fractal and chaos properties in rainfall. In this work, we present a singularity spectrum of a rainfall time series to provide strong evidence of multifractality. A curdling cascade process in a well-developed turbulence is presented as a candidate to describe the rainfall, and the analogy between the rainfall and turbulence is confirmed via the validity of the binomial multiplicative process for describing both systems. The multifractal structure of the temperature and the humidity is investigated in seven cities of Korea. For our cases, we estimate the generalized Hurst exponent, the Renyi exponent, and the singularity spectrum from tick data of the temperature and the humidity. We mainly discuss the different values of the scaling exponent characterizing the multifractality from the hourly data for thirty years. To analyze the multifractality of the temperature and the humidity, we compare the multifractal properties of seven cities (Gwangju, Mokpo, Busan, Seoul, Cholwon, Gangrung, and Sokcho) from our results and discuss the unusual statistical behavior of each city. Aircraft campaigns for the meteorological and environmental research have been conducted in regional and global scales. The aircraft is increasingly considered as one of the best platforms to get the atmospheric three-dimensional information, especially over sea. We discuss the airborne observation plan and payloads designed for the aircraft campaigns over the Korean Peninsula. The main goals of the campaigns are to (i) conduct precipitation (snow) enhancement experiments with observations of the microphysical properties of clouds, dominantly in winter, (ii) monitor the severe weather generally in summer, (iii) characterize the climate change composition and the outflow of pollution from the Asian continent of the troposphere over the Korean Peninsula generally in spring or fall, and (iv) validate satellite and ground-based remote measurements of tropospheric composition generally in spring or fall. We find that the baduk game can be described in terms of multifractals via a generalized dimension and a scaling exponent. For our case, the generalized dimension and scaling exponent can be estimated numerically from the black and mixed (black and white) stones provided the area form of the baduk game in which we assume that the structure is presented in terms of the self-similar structure. We particularly find that the fractal dimension has a much larger value and that the dynamical behavior becomes much more chaotic, as the area increases. We study the dynamical behaviors of the seismicity phenomenon in a complex seismic time series, which presently is of interest from the viewpoint of complex systems. The dynamical mechanism for the aftershock of the 2008 Sichuan earthquake is analyzed and simulated. We mainly treat the correlation and the network structure in a seismic data series. In particular, our result is compared to other findings. We study the evolution of probability distribution functions of returns, from the tick data of the Korean treasury bond (KTB) futures and the S&P 500 stock index, which can be described by means of the Fokker？Planck equation. We show that the Fokker？Planck equation and the Langevin equation from the estimated Kramers？Moyal coefficients can be estimated directly from the empirical data. By analyzing the statistics of the returns, we present quantitatively the deterministic and random influences on financial time series for both markets, for which we can give a simple physical interpretation. We particularly focus on the diffusion coefficient, which may be important for the creation of a portfolio. In this paper, we investigate numerically and analytically the diverse models in the complex system. In sections 2 and 3, we treat the multifractal analysis of the rainfall, the temperature and the humidity in Korean Peninsula, as the atmospheric phenomena. In section 4, we analyze the strategy for the meteorological and environmental sirborne observations over Korean peninsula. Generally, we investigate the scaling behaviors of multifractals in two-dimensional structures in section 5. In section 6, we treat the dynamical behavior of the earthquake structures in the seismicity. In section 7, we analyze the dynamical stochastic processes of the financial markets in the econophysical field. In last section, we remark the summary and the conclusion in our models.