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 (γ) 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 γ 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 γ. My results therefore reveal a previously unconsidered aspect of system stability that is likely to be pervasive across all realistic complex systems.
Highlights
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
I have shown that the stability of complex systems might often be contigent upon variation in the response rates of their individual components, meaning that factors such as rate of trait evolution, transaction speed, or communication speed need to be considered when investigating the stability of complex systems
Variation in component response rate is more likely to be critical for stability in systems that are especially complex, and it can increase the probability that system stability is observed above that predicted by May’s1 classically derived σ SC criterion
Summary
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. 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. In 1972, May[1] first demonstrated that randomly assembled systems of sufficient complexity are almost inevitably unstable given infinitesimally small perturbations Complexity in this case is defined by the size of the system (i.e., the number of potentially interacting components; S), its connectance (i.e., the probability that one component will interact with another; C), and the variance of interaction strengths (σ2)[2]. I show that, despite higher σ, realistic complex systems (in which S is high but finite) are more likely to be stable if their individual component response rates vary. My results are robust across commonly observed network structures, including random[1], small-world[16], scale-free[17], and cascade food web[18,19] networks
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