cs.CYMar 10, 2026

Stability of AI Governance Systems: A Coupled Dynamics Model of Public Trust and Social Disruptions

Authors: Jiaqi Lai, Hou Liang, Weihong Huang

Organizations: Nanyang Technological University, Singapore

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Abstract

AI systems are increasingly entrenched in public governance, yet scholarship lacks formal tools to determine when deviations of public trust in algorithmic institutions dissipate and when they grow into collapse. Stability refers here to asymptotic recovery from finite state perturbations under fixed structural parameters. We address this gap by developing a mathematical framework for institutional trust stability that couples a Friedkin-Johnsen opinion dynamics process with a Hawkes-inspired intensity process for AI controversies. Motivated by the Computers-Are-Social-Actors literature and recent studies of trust in large language models, this bidirectional coupling reveals that governance stability depends on the structural architecture of the information environment rather than absolute trust levels. We derive an exact spectral stability criterion delineating resilience from collapse, demonstrating how event self-excitation and memory persistence systematically narrow the stable parameter regime. Our structural analysis yields four counterintuitive structural implications: high-trust systems can be structurally fragile, low-trust environments can be structurally stable, dynamical stability neither measures nor guarantees algorithmic fairness or legitimacy, and network topology reshapes equilibrium heterogeneity while its effect on spectral stability is uniformly bounded in an explicit memory-dominated regime. Governance assessment should therefore pair normative evaluation of harms and fairness with structural analysis of recoverability, rather than treating either as a proxy for the other.

Figures & tables

Figure 1: Coupled dynamics between trust TtT_{t} and perceived event intensity StS_{t} . The memory state accumulates as Ht+1=γHt+αTt+βStH_{t+1}=\gamma H_{t}+\alpha T_{t}+\beta S_{t} and the event intensity is read out as St+1=μ+Ht+1S_{t+1}=\bm{\mu}+H_{t+1} (Eq. 2); events feed back into trust through BStBS_{t} (Eq. 1).
SymbolDescription
TtT_{t}Institutional trust vector at time tt , ∈Rn\in\mathbb{R}^{n}
StS_{t}Perceived controversy intensity vector, ∈Rn\in\mathbb{R}^{n}
HtH_{t}Aggregated memory state, ∈Rn\in\mathbb{R}^{n}
AADiagonal susceptibility matrix (FJ model)
BBDiagonal reactivity matrix
WWInfluence/adjacency matrix encoding information
Table 1: Summary of notation.
Figure 2: Simulated trust and event trajectories ( T=50T=50 ). Dashed horizontal lines mark the analytical fixed point (T∗,S∗)(T^{*},S^{*}) from Eq. (5); the simulated dynamics converge onto it.
Figure 3: Sensitivity of β\beta ( γ=0.5, α=0.05\gamma=0.5,\ \alpha=0.05 ). The dashed line marks ρ(J2n)=1\rho(J_{2n})=1 , crossed at β∗≈0.50\beta^{*}\approx 0.50 , and the shaded region is divergent. Each point is a separate fixed-parameter system: the sweep traces a boundary in parameter space, not a shock-induced transition within one trajectory.
Figure 4: Effect of network topology on trust–event dynamics ( n=10n=10 ), with identical draws of AA , BB , T0T_{0} , T1T_{1} across columns. Columns: Random, Echo Chamber (trajectories colored by group), Star/KOL (hub in black). Top: trust trajectories; middle: event intensities; bottom: WW heatmap. A one-step pulse of magnitude ΔH=0.45\Delta H=0.45 is applied to event memory at t=25t=25 (vertical dashed line); all three systems return toward equilibrium, consistent with ρ(J2n)=0.849<1\rho(J_{2n})=0.849<1 . The pulse tests recovery under a fixed Jacobian and does not change the spectral regime.
Figure 5: Topology sensitivity across the β\beta sweep ( γ=0.5\gamma=0.5 ; critical β∗ ⁣≈ ⁣0.50\beta^{*}\!\approx\!0.50 ) and the γ\gamma sweep ( β=0.35\beta=0.35 ; critical γ∗ ⁣≈ ⁣0.65\gamma^{*}\!\approx\!0.65 ). The three curves separate at lower memory strength, confirming that fixed WW enters the spectrum, but nearly overlap as the common memory term dominates near the reported boundary. The latter is the empirical signature of the conditional topology–stability bound in Implication 4 and Theorem S1, not universal topology invariance.
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