Research Article Modeling Complex Systems by Structural Invariants Approach Jiri Bila , Ali. H. Reshak , and Jan Chysky Czech Technical University in Prague, Institute of Instrumentation and Control Engineering, Technicka 4, 166 07 Prague 6, Czech Republic Correspondence should be addressed to Jiri Bila; jiri.bila@fs.cvut.cz Received 11 December 2020; Revised 13 June 2021; Accepted 19 July 2021; Published 6 September 2021 Academic Editor: Chrystopher L. Nehaniv Copyright © 2021 Jiri Bila et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. When modeling complex systems, we usually encounter the following difficulties: partiality, large amount of data, and uncertainty of conclusions. It can be said that none of the known approaches solves these difficulties perfectly, especially in cases where we expect emergences in the complex system. e most common is the physical approach, sometimes reinforced by statistical procedures. e physical approach to modeling leads to a complicated description of phenomena associated with a relatively simple geometry. If we assume emergences in the complex system, the physical approach is not appropriate at all. In this article, we apply the approach of structural invariants, which has the opposite properties: a simple description of phenomena associated with a more complicated geometry (in our case pregeometry). It does not require as much data and the calculations are simple. e price paid for the apparent simplicity is a qualitative interpretation of the results, which carries a special type of uncertainty. Attention is mainly focused (in this article) on the invariant matroid and bases of matroid (M, BM) in combination with the Ramsey graph theory. In addition, this article introduces a calculus that describes the emergent phenomenon using two quantities—the power of the emergent phenomenon and the complexity of the structure that is associated with this phenomenon. e developed method is used in the paper for modeling and detecting emergent situations in cases of water floods, traffic jams, and phase transition in chemistry. 1. Introduction e field of complex systems is proving to be a much needed field of research. In this article, we focus mainly on modeling complex systems and processing emergent situations. Many approaches have been used for modeling complex systems until now and here we introduce some of them: Multi-agent and cellular automata approach [1, 2] Physical approach [3] Probability and statistical approach [4] State approach [5, 6] Complexity and entropy approach [7–9] Structural invariant approach [10] Simulation approach [11, 12] Each of the introduced approaches has advantages and disadvantages and could be characterized by many pages. In this article, we concentrate especially on emergent be- havior and emergent situations in complex networks of transport and hydrological systems and on systems of material physics and chemistry. is article has been inspired, among other sources, by the book, “A Different Universe (Reinventing Physics from the bottom down), by Robert B. Laughlin (Nobel Prize winner)” [13]. Laughlin introduces “emergence as an orga- nization principle” and from this point of view explores a wide field of physics. e whole book leads to the following opinion: “If we accept the world with emergence, we also announce the end of reductionism. (at is—the end of the time when we thought that everything essential in the world could be calculated.)” is means that when studying such systems, there is always a certain part of the events that we cannot calculate. In this article, we try to estimate (qualitatively) how big this part of the story is, which we cannot calculate. As will Hindawi Complexity Volume 2021, Article ID 6650619, 17 pages https://doi.org/10.1155/2021/6650619