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By José Balsa-Barreiro, Aymeric Vié, et al. :

"The complexity of systems refers to the diversity and heterogeneity of behaviors at multiple scales, ranging from individuals to communities or societies at large. The addition of interdependencies increases the number of potential relationships among the system parts, enabling the emergence of new types of association and more elaborate behaviors. Interdependencies are the basis for the emergence of collective capabilities that would otherwise be unfeasible. Individuals associate with one another by coupling their behaviors to increase the space of possibilities of the whole system at a larger scale.

However, adding interdependencies has a hidden downside. The more connected a system is, the easier is for errors and unexpected detrimental behaviors to propagate across the system. Interdependencies create new paths for error propagation and may escalate the risks of malfunctions in both frequency and severity (Newman et al., 2006). Anomalies do not grow or occur linearly. Their magnitude may explode given the existence of critical masses and tipping points during networked propagation processes. Analyzing systemic failure exceeds traditional research methods that simplify reality by analyzing errors in isolation.

Material science and mechanical engineering consider this kind of failure. A mechanical structure becomes more vulnerable to future shocks when multiple loads are continuously applied to them. The structure crashes when the load forces overcome the resistance threshold of any part or material, which becomes more sensitive due to the repeated load forces. A fatigue process that results from the establishment of interdependencies among the material parts after exceeding certain thresholds explains this system failure.

A system with a great number of interdependencies can be extremely vulnerable to malfunctions, even if it does not come from the most important nodes. The chaos theory, which is inherent to complex systems, explains that small variations may entail huge changes in entire systems. Similarly, any potential malfunction can effortlessly cascade across the whole system and affect its functional behavior. Some concrete examples related to these effects are appreciated in very different kinds of systems, both with natural and human inception. Natural events such as forest wildfires or the consequences of earthquakes in some regions eventually manifest catastrophic dimensions and huge regional differences that go beyond the phenomenon itself (Balsa-Barreiro and Hermosilla, 2013)." (