Complex Systems: Chaos and Beyond: A Constructive Approach by Professor Kunihiko Kaneko, Professor Ichiro Tsuda (auth.)

By Professor Kunihiko Kaneko, Professor Ichiro Tsuda (auth.)

Chaos in technological know-how has consistently been a desirable realm because it demanding situations the standard clinical process of reductionism. whereas conscientiously distinguishing among complexity, holism, randomness, incompleteness, nondeterminism and stochastic behaviour the authors express that, even though many points of chaos were phenomenologically understood, such a lot of its defining ideas are nonetheless tricky to understand and formulate. Demonstrating that chaos escapes all conventional tools of description, the authors got down to locate new the right way to care for this phenomenon and illustrate their optimistic procedure with many examples from physics, biology and knowledge expertise. whereas holding a excessive point of rigour, a very advanced mathematical gear is shunned so as to make this booklet available, past the professional point, to a much broader interdisciplinary readership.

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G. 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.

G. 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.

Then many other ants gather there because they are attracted by the pheromone, and they in turn produce the pheromone. This positive feedback forms a path of pheromone leading to the food. Such a path of pheromone is the "top level" , and once this path is formed, the ants move along the path. At this stage, the bottom level (the behavior of an individual ant) is dominated by the top level. However, when the food has gone, the path disappears. Hence it is possible to make a path to the nearest source of food and to erase it in turn.

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