Reaction Networks as a Language for Systemic Modeling: On the Study of Structural Changes

Abstract

Reaction Networks have been recently proposed as a framework for systems modeling due to its capability to describe many entities interacting in contextual ways and leading to the emergence of meta-structures. Since systems can be subjected to structural changes that not only alter their inner functioning, but also their underlying ontological features, a crucial issue is how to address these structural changes within a formal representational framework. When modeling systems using reaction networks, we find that three fundamentally different types of structural change are possible. The first corresponds to the usual notion of perturbation in dynamical systems, i.e., change in system's state. The second corresponds to behavioral changes, i.e., changes not in the state of the system but on the properties of its behavioral rules. The third corresponds to radical structural changes, i.e., changes in the state-set structure and/or in reaction-set structure. In this article, we describe in detail the three types of structural changes that can occur in a reaction network, and how these changes relate to changes in the systems observable within this reaction network. In particular, we develop a decomposition theorem to partition a reaction network as a collection of dynamically independent modules, and show how such decomposition allows for precisely identifying the parts of the reaction network that are affected by a structural change.

The Complexity–Stability Debate, Chemical Organization Theory, and the Identification of Non-classical Structures in Ecology

“…Second, it is necessary to develop measures of stability indicators such as resilience, robustness, adaptivity and so in the language of reaction networks. In [70] and [24] some ideas have been advanced in this respect. Third, it is important to extend COT to represent ecological interactions in space.…”

“…When a structural perturbation occurs the organizational structure itself is modified. A decomposition theorem for organization allows to identify the parts of the organizational structure that are affected by the structural perturbation, and thus different algorithms have proved that computing the organizational structure is feasible for reactions networks of hundreds or even thousands of species [8,70,72].…”

“…In particular, since organizations at the higher levels of the hierarchy can be understood as combinations of organizations at lower levels, COT relates the recursive structure of organizations to the stability of the reaction network. For example, in [70] it is shown that organizations function in dynamically independent modules, and some of these modules are more fragile to perturbations than others, while in [72] it is found that the dynamical analysis of a certain organizations can be disregarded because their dynamical properties can be obtained from the dynamics of the smaller organizations that are contained in them. In this vein, complexity indicators such as synergy and non-decomposability have been developed to better understand those cases.…”

Goal Directedness, Chemical Organizations, and Cybernetic Mechanisms

“…Namely, a goal might be reached by the parallel (or weakly coupled) work of different units. This can be represented using reaction networks by dynamical decomposition methods which allow to disentangle the dynamics of the network into independent parts [32,42].…”

“…Moreover, in [28], Theorem 1 is extended to other stable asymptotic behaviors such as periodic orbits and limit cycles. In addition to these results, necessary conditions for the existence of adequate processes, and their relation to other theories that connect structure and dynamics such as Petri-Nets and Deficiency theory, are explored in [14,15,29], and algorithmic studies concerning the computation of the organizations of a reaction network are presented in [30][31][32][33][34].…”