Evolution of complex systems with hyperbolic distribution - Делас, Николай Иванович (Eastern-European Journal of Enterprise Technologies, 2013)
Most complex, hard-formalized systems with a large number of elements can be viewed as objects on a finite set of "carriers" of which a limited set of "resources" is distributed. The hyperbolic distribution is characteristic for systems where "resources" are more dynamic than "carriers", i.e. the relaxation time of "resources" is much less than the relaxation time of "carriers." The application of the principle of maximum entropy permits to obtain expressions for the maximum hyperbolic distribution law (11), which at certain values of its parameters asymptotically approaches to the hyperbolic. The evolution of a complex object in time is expressed in a change of its distribution curve. The process of evolution looks like a quasi-equilibrium motion of the system to a state of complete equilibrium, when the maximum is reached not only by the entropy of "resources" , but also by the entropy of "carriers". The parameter ,being an important characteristic of the system, reflects the evolution of the process. The systems close to a purely hyperbolic distribution (with ) are young systems. They have reached a quasi-equilibrium distribution of "resources", but are far from the state of total equilibrium due to slower settling of "carriers." With increase of the age of the system, the parameter increases, and the distribution curves change as shown at the Fig.4. An algorithm for determining for different time values in the range was described