A Quantitative Description of Nature

  • Igor Grabec
  • Wolfgang Sachse
Part of the Springer Series in Synergetics book series (SSSYN, volume 68)


One of the most important characteristics of Nature is its non-uniformity. If it were homogeneous and stationary there would be no distinct objects or events and no life. The inhomogenity of Nature extends from the subatomic to the cosmic scales and the nonstationarity includes events whose characteristic times range over all time scales. The non-uniformity of Nature is observable in the variations of different properties of Nature in space and time. The most widely used variables for their physical description are the mass density, the chemical composition of substances, pressure, temperature, and mass flow distribution, among others. Because of the spatial and temporal fluctuations of these variables, various dynamic phenomena occur in Nature. Weather phenomena and the growth of living systems are just two examples. Any dynamic phenomenon in Nature can be related to a flow or exchange of energy between parts of a system. For some natural phenomena, this exchange of energy occurs smoothly and quasistatically, but in many cases, when the exchange of energy is increasing, a sudden transition in the behavior and structure of the system is observed. [5, 11, 17, 23] In this new state, the dynamic behavior dominates the structure of the system. In those cases in which the exchange of energy is high, the exchange may occur with strong fluctuations.


Neural Network Information Processing System Natural Phenomenon Quantitative Description Sigmoidal Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Igor Grabec
    • 1
  • Wolfgang Sachse
    • 2
  1. 1.Faculty of Mechanical EngineeringUniversity of LjubljanaLjubljanaSlovenia
  2. 2.Theoretical and Applied MechanicsCornell UniversityIthacaUSA

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