  Fluid flow networks are ubiquitous and can be found in a broad range of
contexts, from human-made systems such as water supply networks to living
systems like animal and plant vasculature. In many cases, the elements forming
these networks exhibit a highly non-linear pressure-flow relationship. Although
we understand how these elements work individually, their collective behavior
remains poorly understood. In this work, we combine experiments, theory, and
numerical simulations to understand the main mechanisms underlying the
collective behavior of soft flow networks with elements that exhibit negative
differential resistance. Strikingly, our theoretical analysis and experiments
reveal that a minimal network of nonlinear resistors, which we have termed a
`fluidic memristor', displays history-dependent resistance. This new class of
element can be understood as a collection of hysteresis loops that allows this
fluidic system to store information. Our work provides insights that may inform
new applications of fluid flow networks in soft materials science, biomedical
settings, and soft robotics, and may also motivate new understanding of the
flow networks involved in animal and plant physiology.
