Measures of complexity of chaotic time series and their application

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Introduction A large number of systems in nature such as the climate, brain, social networks, nervous system, financial markets etc.are termed as complex systems. Understanding the form and function of such systems is currently a focus area of interdisciplinary research involving almost all branches of science (Special issue on complex systems, Science, 1999). Yet, no clear definition of complex systems exists. These are systems that by design or function or both are difficult to understand and verify (Weng et al., 1999). Such systems contain interaction among many interconnected parts. Although we may have a clear understanding of the individual components, the complex structure and the constant evolution makes it difficult to fully understand the system as a whole. Some of the complex systems are also adaptive in nature, i. e., they constantly change through interaction with the outside. Examples of complex adaptive systems are the brain, social networks, financial markets etc.. For any specific complex system, physicists aim to understand the underlying dynamics and obtain a set of equations which could model the system. Our understanding of many body interactions, statistical mechanics and nonlinear dynamics are particularly useful in this effort. One such method of understanding the dynamics of complex systems is to examine a sequence of observations.