Modeling of Complex Systems by Means of Partial Algebras

Abstract

Complex systems are very hard to describe by some unified language and calculus. In cases when their nature is very heterogeneous is possible to use with advantage state description. Formalization of operations on the set of states usually leads to partial algebras. The work with partial algebras is rather difficult and unpractical. From this reason some methods approximating partial algebras by some more symmetrical objects are searched for. In this paper there is proposed an approximation of this algebras by free cyclic groups. Then using the combination of Matroid Theory and Ramsey theory of graph the prediction of a possible appearance of emergent situation is executed. Data and knowledge used in the paper for the demonstration of developed method application are from the field of Ecology.

Keywords

• partial algebras
• cyclic groups
• qualitative distance
• matroid
• matroid bases
• prediction of emergent situation on complex system