“Simply” Modelling Complex Systems

Complex systems are everywhere: living organisms, ecosystems, financial systems, computing systems, and more. The stability of these systems is something that we take for granted, as we assume that living things won’t suddenly die without warning or that ecosystems won’t suddenly collapse. Complex systems are groups of interacting components, however there are enough interacting components that even if we can predict how each component operates by itself (e.g. cells in our body, financial transactions) we cannot easily predict how a system of interacting components will behave (e.g. our bodies, the global economy).

There has been a long standing debate on what makes complex systems such as these stable. One argument is that diversity in the components of a complex system make it more resilient, and therefore more stable, under the influence of disturbances. The second argument is that greater diversity increases the complexity of the system and makes it more likely to collapse, since there are more opportunities for components of the system to break down. Fyodorov and Khoruzhenko (2016, PNAS 113:6827-6832) sought to study the collapse of complex systems using a simplified mathematical model. Through their analysis, Fyodorov and Khoruzhenko find that as the diversity of a system increases, the proportion of stable states decreases.

The model developed by Fyodorov and Khoruzhenko considers only randomly assembled, randomly interacting components. While their model may imply that diversity in complex systems such as ecosystems could introduce instabilities, biological systems and financial systems are not randomly assembled or randomly interacting. Further work on specifying their model for non-random systems may reveal insights into how ecosystems are structured and resist disturbance, and how to predict the dynamics of such complex systems.

Stay safe and stay informed,
Joe

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