Topological Memory and Hysteresis in Reconfigurable Dusty Plasma Networks

Complex systems frequently exhibit emergent behaviour arising from the evolving topology of interactions between constituent elements. Dusty plasmas provide a uniquely accessible physical platform for investigating this phenomenon because long-range electrostatic interactions continuously reorganise the connectivity of the underlying interaction network. This study examines how changes in the Debye screening length ($\\lambda_D$) modify graph topology, latent-state geometry, and memory formation within a full E(3)-equivariant Yukawa particle system. Graph-theoretic analysis demonstrates that modulation of $\\lambda_D$ induces a structural percolation transition that reorganises the connectivity of the interaction network. A multimodal VAE-EGNN encoder compresses these topological changes into a low-dimensional latent representation, with the dominant principal component capturing the majority of latent variance and exhibiting strong correlation with graph percolation metrics. Dynamic Mode Decomposition with control and standard reservoir-computing benchmarks reveal limited evidence for useful nonlinear computation, indicating that the system does not behave as a conventional computational reservoir. In contrast, topology-history analysis, latent-manifold investigation, and reversible Debye-length sweeps reveal consistent evidence of path dependence and structural memory. Identical values of the Debye screening length produce measurably different topological and latent states depending upon the trajectory through parameter space. Ensemble hysteresis studies confirm reproducible loop-area formation across independent random seeds, demonstrating that information about previous configurations is retained within the evolving interaction topology of the plasma. A recent sweep-rate study reveals that while the hysteresis loop area decreases as the modulation rate slows, the enclosed area converges toward a finite non-zero value ($\\approx 2.50$) rather than vanishing. This residual area provides strong evidence of persistent topological remanence encoded within the interaction network, distinct from mere transient viscous lag. The outcome suggests that the dusty plasma behaves more like a path-dependent topological memory medium than a nonlinear computational reservoir.