Resource-limited complex systems are ubiquitous in the natural world, as is the potential for instability in such systems. Classic models of interacting species have provided a basis for our understanding of stability in these systems, and suggest that stable coexistence requires weak, rare, and asymmetric interactions. But missing from these models is an explicit understanding of how resource exchange and resource limitation can drive or prevent instability. Here, we show that systems based on general rules for the consumption and exchange of resources are guaranteed to be stable when exchange of resources is reciprocated by each pair of partners. These cooperative, mutualistic interactions can be arbitrarily strong and yet not disrupt stability. More general modes of exchange will lead to instability when supply rates are low, but when resource supply from outside the system is sufficiently high, arbitrary exchange is consistent with a stable equilibrium.

中文翻译：

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资源受限环境中复杂系统的合作与稳定性

资源有限的复杂系统在自然世界中无处不在，这种系统可能会造成不稳定。相互作用物种的经典模型为我们理解这些系统的稳定性提供了基础，并表明稳定的共存需要弱，稀有和不对称的相互作用。但是这些模型中缺少对资源交换和资源限制如何驱动或防止不稳定的明确理解。在这里，我们表明，当每对伙伴交换资源交换时，可以确保基于资源消耗和交换通用规则的系统是稳定的。这些合作，互惠的互动可以任意强加，但不会破坏稳定性。供应率较低时，更通用的交换方式会导致不稳定，