The fluidic memristor: collective phenomena in flow networks of negative differential resistance

Flow networks are essential for both living organisms and engineered systems. Very often they are successfully modeled as networks of linear resistors, however, in the animal and plant circulatory system, the resistance of each element can be highly nonlinear. In some cases, it can even present regions of negative differential resistance, where the flow decreases as the pressure difference increases. Inspired by these systems, we have proposed a mathematical model for nonlinear flow networks of any topology, it includes nonlinear resitors and allows for internal accumulation/depletion of volume [1]. This model displays a wide variety of complex phenomena such as self-sustained oscillations, excitability and memory effects. We will describe this phenomenology and show how we are building such systems in the lab, where we exploit fluid-structure interactions to build tunable valves that can be arranged to create nonlinear flow networks. Finally, we will discuss an experimental system that behaves as a fluidic memristor.

[1] M Ruiz-García, E Katifori, Emergent dynamics in excitable flow systems, Physical Review E 103 (6), 062301 (2021)