Component response rate variation underlies the stability of highly complex finite systems

TL;DR

This study demonstrates that variation in component response rates significantly enhances the stability of highly complex systems, challenging traditional views that increased size and interconnectivity reduce stability.

Contribution

It introduces the novel insight that response rate variation across components can promote stability in complex systems, a factor previously overlooked in stability analyses.

Findings

Response rate variation increases system stability.

Stability benefits are consistent across network types.

Highly complex systems rely on response variation for stability.

Abstract

The stability of a complex system generally decreases with increasing system size and interconnectivity, a counterintuitive result of widespread importance across the physical, life, and social sciences. Despite recent interest in the relationship between system properties and stability, the effect of variation in response rate across system components remains unconsidered. Here I vary the component response rates ($\boldsymbol{\gamma}$) of randomly generated complex systems. I use numerical simulations to show that when component response rates vary, the potential for system stability increases. These results are robust to common network structures, including small-world and scale-free networks, and cascade food webs. Variation in $\boldsymbol{\gamma}$ is especially important for stability in highly complex systems, in which the probability of stability would otherwise be negligible. At such extremes of simulated system complexity, the largest stable complex systems would be unstable if not for variation in $\boldsymbol{\gamma}$. My results therefore reveal a previously unconsidered aspect of system stability that is likely to be pervasive across all realistic complex systems.