A unified predictive model is introduced that accurately estimates how structural and behavioral parameters determine the time required for complete adoption, showing that mobility is the dominant accelerator while memory and connectivity modulate convergence in systematic ways.
Abstract
Tipping-point dynamics describe the critical conditions under which a committed minority drives a population to abandon an established convention in favor of a new one. We present a transparent agent-based model of this process, in which agents hold one of two behavioral states and a mobile committed minority attempts to overturn the incumbent convention. Our goal was to examine how localized mobility, bounded agent memory, and network topology jointly influence the tipping threshold. Using a custom agent-based simulation framework, we found that in many configurations, tipping becomes effectively inevitable: given sufficient time, the population always converges to the minority state. This observation motivated a complementary analysis focused on the pace of convergence rather than its feasibility. We introduce a unified predictive model that accurately estimates how structural and behavioral parameters determine the time required for complete adoption, showing that mobility is the dominant accelerator while memory and connectivity modulate convergence in systematic ways. Together, these results extend classical tipping-point research by linking structural and behavioral factors not only to the likelihood of convention change but also to the timescale on which it unfolds. While we frame the model in terms of convention-like binary behavioral adoption, the same mechanisms bear on norm change and other contagion-like social processes.
This work forms a correction-aware network model that tracks susceptible, exposed, infectious, and corrected agents and derive its early-invasion condition for heterogeneous communication networks, and couple this propagation model to an analytic majority-vote benchmark in which a clean-task reliability target imposes a minimum connectivity requirement.
It is shown that simple persistence-based opinion-dynamics models reproduce collective outcomes in all-generalist LLM populations, whereas heterogeneous LLM populations require population-level belief composition to reproduce consensus and agent identity to predict individual belief transitions.
Germans Savcisens, Samantha Dies, Courtney Maynard et al.· arXiv.org· 1 citation
We formulate a statistical physics framework to model a networked stochastic dynamical system exhibiting bistability, driven by additive noise and social conformity. We apply this model to understand and mitigate AI-induced delusional spiraling-a phenomenon where algorithmic sycophancy from Large Language Models continuously reinforces inaccurate beliefs within a socially interacting society. By partitioning the network into a majority of regular agents and a minority of"aware"nodes (Teachers) placed at topological hubs, we use a degree-weighted mean-field approximation to reduce high-dimensional coupled Langevin equations into a single macroscopic drift equation. We provide a closed-form analytical derivation for the deterministic critical tipping time through a saddle-node bifurcation. We validate this analytical boundary using finite-size scaling and demonstrate a universal data collapse across diverse network topologies. Finally, we optimize an intervention strategy under a strict budget constraint that balances the topological footprint against driving velocity. We prove mathematically that under certain conditions, a highly concentrated, rapid intervention targeting massive hubs strictly outperforms a distributed, slow approach to rescue the network.
Sayantari Ghosh, Saumik Bhattacharya, P. Chakrabarti· arXiv.org· 0 citations
Large language models (LLMs) are increasingly adopted as closed-loop controllers in physical multi-agent systems, yet their emergent collective dynamics remain incompletely characterised. We deploy 22 LLM agents as direct, real-time target-speed controllers (per 0.5 s cycle, with IDM as collision-avoidance clamp) on a 230 m ring road under the Sugiyama 2008 paradigm, reproducing human-like stop-and-go waves. Six matched controls spanning stochasticity (white noise, OU noise, temperature), population variance, and dynamical instability (delay, OV model) are systematically excluded. The surviving phenomenon, termed Sustained Heterogeneity (SH), is the persistent, approximately temperature-insensitive (approx. 8 percent across a 6x T sweep), per-cycle divergence in LLM-chosen target-speed adjustments, propagating through a three-stage cascade of drift, gap erosion, and nonlinear braking. Across four traffic densities, the critical LLM penetration fraction p_c decreases monotonically from no transition at density 43.5 veh/km to p_c approx 0.23 at density 95.7 veh/km, consistent with an initiation-threshold model governed by trigger distance, stochasticity, and fleet size. Chain-of-thought analysis of 39,600 decisions across three seeds shows agents engage in multi-factor safety reasoning, yet systematic divergence persists, implying stability must be enforced at the dynamics layer. This is the first study to identify a previously uncharacterised collective mechanism in LLM-controlled traffic and map a density-dependent phase boundary p_c(rho).
We introduce a majority-rule model in which collective reversal can be activated in highly aligned groups even when a limited number of members dissent. The dissent tolerance $d$ extends the strict-unanimity dynamics by making near-unanimous group compositions eligible for reversal. Mean-field analysis and simulations reveal that this change qualitatively alters the phase structure. Under strict unanimity, a physically accessible transition exists only for $n=3$ and $n=4$. Allowing dissent restores transitions at larger interaction sizes, replacing the fixed interaction-size threshold with an accessibility boundary in the $(n,d)$ plane. When the activation window is sufficiently broad, directional asymmetry can eliminate one of the two ordered attractors through a saddle-node bifurcation, producing a single stable collective state. In the one-sided case, increasing the dissent tolerance can shorten the transient approach to consensus but leaves its leading logarithmic dependence on population size unchanged. Activation selectivity acts as an independent control parameter for collective ordering, bistability, and consensus dynamics.
Roni Muslim, Rinto Anugraha Nqz, Qonuni Gusthaf Haq et al.· 0 citations
A novel framework for modeling binary opinions of individuals connected through a weighted directed network, where edge weights quantify interpersonal influence is proposed, which allows individuals to update their biases using structured memory sets that capture limited and delayed information exchange.
