Towards an Analytic Framework for System Resilience Based on Reaction Networks

Reaction network is a promising framework for representing complex systems of diverse and even interdisciplinary types. In this approach, complex systems appear as self-maintaining structures emerging from a multitude of interactions, similar to proposed scenarios for the origin of life out of autocatalytic networks. The formalism of chemical organization theory (COT) mathematically specifies under which conditions a reaction network is stable enough to be observed as a whole complex system. Such conditions specify the notion of organization, crucial in COT. In this paper, we show that the structure and operation of organizations can be advanced towards a formal framework of resilience in complex systems. That is, we show that there exist three fundamental types of change (state, process, and structural) defined for reaction networks, and that these perturbations not only provide a general representation of perturbations in the context of resilience but also pave the ground to formalize different forms of resilient responses. In particular, we show that decomposing the network's operational structure into dynamically decoupled modules allows to formalize what is the impact of a perturbation and to what extent any potential compensation to that perturbation will be successful. We illustrate our approach with a toy model of a farm that operates in a sustainable way producing milk, eggs, and/or grains from other resources. With the help of simulations, we analyze the different types of perturbations and responses that the farm can undergo and how that affects its sustainable operation.