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.
We study a society of agents belonging to a number of occupational or cultural groups that form opinions about others' situation in the same or different group. Opinions develop either by observation within own group or by directly interacting with members of other groups, therefore by word of mouth (WoM). Additionally, global mass media (MM) may be available that inform indirectly about the situation of the various groups. The sociocultural interplay of these processes and the degrees of relative exposure to each of the sources has diversified effects on final opinion and social attitude formation. In large and complex societies and groups where not everyone can physically interact by WoM with everyone about everything, these processes show potential for mass control and social automation engineering. Our model can also represent and be generally informative about segmented societies that consist of groups with different occupational and cultural characteristics and it can offer insights into social issues such as the generation gap, social cleavages and so on.