The fluidic memristor: collective phenomena in elastohydrodynamic networks

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. 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. 

We proceed to show theoretically how complex flow networks with non-linear pressure-flow relationship show excitability, without any inherent oscillatory or excitable behavior at the nodes. In the absence of any time dependence in the pressure input and output we observe emerging dynamics in the form of self-sustained waves, which travel through the system. The frequency of these waves depends strongly on the network architecture and it can be explained with a topological metric.