By Professor Kunihiko Kaneko, Professor Ichiro Tsuda (auth.)
Chaos in technological know-how has continuously been a desirable realm because it demanding situations the standard medical strategy of reductionism. whereas conscientiously distinguishing among complexity, holism, randomness, incompleteness, nondeterminism and stochastic behaviour the authors convey that, even if many points of chaos were phenomenologically understood, so much of its defining ideas are nonetheless tough to understand and formulate. Demonstrating that chaos escapes all conventional tools of description, the authors got down to locate new the way to care for this phenomenon and illustrate their confident process with many examples from physics, biology and knowledge expertise. whereas preserving a excessive point of rigour, a very complex mathematical gear is kept away from which will make this e-book obtainable, past the expert point, to a much wider interdisciplinary readership.
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Additional info for Complex Systems: Chaos and Beyond: A Constructive Approach with Applications in Life Sciences
Particles or elements). In the thermodynamic limit in statistical mechanics, important characteristics can be derived by first taking such infinite limit. For example, as with regard to the problem of a phase transition in a thermal-equilibrium system, a singularity in thermodynamic-quantities has appeared only in this 26 1. Necessity for a Science of Complex Systems limit. Though some interesting characteristics, such as the divergence of fluctuations, appear due to the limit itself, still essential characteristics of the phenomena are described by a few order parameters.
For example, to understand muscle contractions, we need a detailed knowledge of the interactions in the actomyosin system. The origin of muscle force, at a molecular level, is due to the sliding between two kinds of proteins, actin and myosin, which form the actomyosin system. As myosin moves along the actin, the muscle, as an assembly of such proteins, contracts, leading to some force. According to recent experiments, this microscopic system can work even at the level of thermal noise. Actin forms a cytoskeleton, and it is known to include structural anisotropy determining the anisotropic potential of the actomyosin system.
In a complex system, we are unable to understand the system's dynamic state fully by an external observation only. As will be discussed later, in complex systems, the observation problem is crucial, and it is necessary to describe a system including its observer [Shaw 1984]. In this respect, Rossler's endophysics will be important in the study of complex systems [Gerbel and Weibel 1992]. 2. 1 Observation Problems of Chaos If chaos could be characterized by one word, it would be "complexity". Even with the greatest of efforts, a finite sequence cannot accurately describe chaos.
Complex Systems: Chaos and Beyond: A Constructive Approach with Applications in Life Sciences by Professor Kunihiko Kaneko, Professor Ichiro Tsuda (auth.)