Collective Behavior and Memory States in Flow Networks with Tunable Bistability

TL;DR

This study demonstrates a tunable electronic platform of bistable, negative-differential-resistance (NDR) edges that mimic flow-network memory. By independently tuning two internal parameters, the device exhibits robust memory at the network level, including emergent memory states, avalanches, and both encoded antiferromagnetic and ferromagnetic interactions. The work develops a geometric and SPICE-based framework to predict state transitions, reveals the role of effective interactions, and shows how to design explicit inter-edge couplings to program network behavior. The results pave the way for engineered memory in complex networks and offer a controllable testbed for exploring memory phenomena beyond the hysteron paradigm.

Abstract

Multistability-induced hysteresis has been widely studied in mechanical systems, but such behavior has proven more difficult to reproduce experimentally in flow networks. Natural flow networks like animal and plant vasculature can exhibit complex nonlinear behavior to facilitate fluid transport, so multistable flows may inform their functionality. To probe such phenomena in an analogous model system, we utilize an electronic network of hysteretic bistable resistors designed to have tunable negative differential resistivity. We demonstrate our system's capability to generate complex global memory states in the form of voltage patterns, which is mediated by the tunable nonlinearity of each element's current-voltage characteristic. We investigate avalanching behavior arising from effective interactions, and demonstrate how to encode explicit interactions of arbitrary form by taking advantage of the tunable circuitry design.

Figures (10)

• Figure 1: Construction of the NDR device. (a) Basic circuit diagram of NDR device highlighting the two tunable parameters, $V_{gg}$ (green) and $R_L$ (blue). In the rest of this work, the NDR device will be represented with a resistor overlaid with a wavy arrow. (b) Breadboard layout of the device. (c) IV characteristics of the NDR device for various values of $R_L$ (left), and $V_{gg}$ (right). (d) Heatmap showing the peak current $I_\textrm{max}$ and valley current $I_\textrm{min}$ as a function of $V_{gg}$ and $R_L$, based on experimental data.
• Figure 2: Geometric solutions of small network interactions between linear and nonlinear elements. (a) Native IV curve for an NDR device. (b) Native IV curve for a linear resistor, $R_0 = 6k \Omega$. (c) Solutions for current in a network with one linear resistor and one nonlinear resistor in series, for various values of $\Delta V_T$. The left column shows the geometric solution of Eq. \ref{['eq:geometric']} and the right column the $I(\Delta V_T)$ for the NDR plus linear resistor circuit. The total $I(\Delta V_T)$ curve shows a hysteresis loop. (d) Solutions for current in a network with one linear resistor and three nonlinear resistors in series, for various values of $\Delta V_T$. The ordering that each nonlinear element switches state is dependent on each curve's peak current, $I_\textrm{max}$. (e) Geometric construction of a branching network. Elements in parallel are stacked vertically, and elements in series are stacked horizonally.
• Figure 3: Demonstration of emergent memory effects in a network of 9 NDR elements in series. (a) Diagram showing network connectivity. The network is held at a total voltage $V_0$, and current is measured with a small resistor $R_0 = 100\Omega$. (b) The IV curves of each of the nonlinear elements have been tuned with respect to each other to control the ordering of state switching. Inset: nominal values of $I_\textrm{max}$ and $I_\textrm{min}$ for each edge. (c-d) Photographs of the network in the states "010111010", which visually represents a "$+$", and "101010101", which visually represents an "$\times$", respectively. The multimeter measures a global drop of $V_0 = 12V$ in both cases. (e-f) Histories of total source voltage ramping $V_0(t)$ (top), as well as the voltage drops of each nonlinear edge $\Delta V_i$ (bottom), to achieve the states "$+$" and "$\times$", respectively. Extrema of $V_0$ are labeled with the binary string achieved at the given time step.
• Figure 4: Avalanches arise from effective network interactions. (a) Schematic of the network. Three NDR edges are arranged in series with one linear resistor, and the network is controlled via the global source voltage, $V_0$. (b) Voltage drops of each edge as $V_0$ is ramped up and then back down. Arrows indicate where edge transitions occur, and states are labeled by their binary sequence. The three purple arrows denote the avalanche. (c) Geometric construction of the network just before (top) and just after (bottom) the avalanche. (d) Transition thresholds and stability of each binary state, obtained from SPICE simulation. Colored arrows indicate the transitions corresponding to the arrows in (b). The avalanching transition passes through two unstable states, 111 and 110. (e) Full transition graph for the network with tunings shown.
• Figure 5: Encoded anti-cooperative interactions result in antiferromagnetic behavior. (a) The gate voltage of each edge, $V_{gg,i}$, is a function of the voltage drop of its neighbor, $\Delta V_{i-1}$. The boxed area shows the voltage adder circuitry which results in $V_{gg,i} = \Delta V_{i-1} + G_\textrm{min}$. Experimental data (b) and analogous SPICE simulation (c) demonstrate the network's antiferromagnetic response. (b) Voltage drops of each edge as a function of the global drive, $V_0$, as it is ramped up and down. Arrows indicate the avalanching transitions from 010 to 101 (red) and from 101 to 010 (blue). (c) Dashed lines indicate snapshots of the simulated network at different binary states in (d-f). The geometric constructions of each snapshot in (c) show how the IV curves of the edges evolve from the 000 (d) to 010 (e) to 101 (f) states. (g) The transition graph for this network summarizes the antiferromagnetic avalanches.