What is a Complex System, After All?

Abstract

The study of complex systems, although an interdisciplinary endeavor, is considered as an integrating part of physical sciences. Contrary to the historical fact that the field is already mature, it still lacks a clear and unambiguous definition of its main object of study. Here, I propose a definition of complex systems based on the conceptual clarifications made by Edgar Morin about the bidirectional non-separability of parts and whole produced by the nature of interactions. Then, a complex system is defined as the system where there is a bidirectional non-separability between the identities of the parts and the identity of the whole. Thus, not only the identity of the whole is determined by the constituent parts, but also the identity of the parts are determined by the whole due to the nature of their interactions. This concept allows, as shown in the paper, to derive some of the main properties that such systems must have as well as to propose its mathematical formalization.

What Is in a Simplicial Complex? A Metaplex-Based Approach to Its Structure and Dynamics

“…For instance, in the simplex shown in Figure 4, we ran the equation ẋ(t) = −Lx(t) with initial condition u(0) = u 0 = 1 in the node V 1 , in the edge (1, 2) and in the triangle (1, 2, 3), and 0 elsewhere. Figure 3 shows the results, where it can be observed that the concentration in the edge (2,3) and in the triangle (3,4,5) take negative values at the beginning of the simulation. Also worrying is the fact that there is not a global steady state for diffusion in the simplicial complex, but the nodes reach an independent consensus state from the steady states reached by edges and triangles, which is equal to 0 in this case.…”

“…In Figure 9, we show the results obtained for the same initial condition used for the results in Figure 3, namely all zeros but on the node 1, the edge (1, 2) and the triangle (1,2,3), where the initial concentration is equal to 1 and distributed uniformly for each of the elements. As can be observed, the diffusion on the simplicial complex modeled as a metaplex shows similar behavior to diffusion in both networks or continuous spaces, reaching all domains in the same steady state, which is the average of the initial condition as required in standard diffusion.…”

“…The complexities of many systems, generically known as complex systems, are manifested not only in their structures and behavior [1,2], but also in the difficulties of defining precisely what they are (see [3] and references therein) and, moreover, by the several ways of representing them [4]. Due to their networked nature, the use of graphs has been ubiquitous in representing complex systems [5,6].…”

Optimizing Urban-Scale Evacuation Strategies Through Disaster Victim Aggregation Modification

“…However, evacuation is a complex system involving many stakeholders and resources. Evacuation is classified as a complex system because the evacuation process component is non-linearly correlated and interrelated [8]. This complexity leads to challenges in increasing the decision-making time in determining the evacuation strategies [9] [10].…”

Democratising Complex System Modelling

“…While defining a complex systems is not straight forward 3 there are two main characteristics of complex systems in general: they are made of a large number of interacting entities or agents and they exhibit a non-intuitive collective behavior 4 . Typically open, natural or social, complex systems are difficult to model because "one has to take into account at least two levels of abstraction (the micro and the macro levels) and the way they interact with each other" 5 .…”