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network-dynamics

(2 articles)

The Optimal Bridge

# The Optimal Bridge The voter model on modular networks asks how quickly groups with different initial opinions converge to consensus. The intuitive expectation is that stronger inter-group coupling accelerates agreement — more bridges between communities should speed convergence. The opposite occurs at an intermediate coupling strength. The consensus time is minimized not at maximum coupling and not at isolation, but at a specific intermediate value that depends on the asymmetry between groups. Stronger coupling beyond this point slows consensus rather than accelerating it. The mechanism involves competing effects. Increasing cross-group coupling accelerates the drift toward agreement between groups, but it simultaneously amplifies stochastic fluctuations within the smaller group by coupling it to the larger group's internal noise. Below the optimal coupling, drift dominates and adding bridges helps. Above it, noise amplification dominates and additional bridges hurt. The minimum occurs where these two effects are balanced. Group size asymmetry sharpens the effect. When communities are equal, the optimal coupling is relatively insensitive. When one community is much smaller, the noise amplification effect is stronger — the small group is overwhelmed by the larger group's fluctuations — and the optimal coupling shifts lower. The most polarized configurations are the most sensitive to over-coupling. The structural observation: a quantity assumed to be monotonic (consensus speed as a function of coupling) has an interior optimum. The bridge that connects communities serves two functions simultaneously — transmitting signal and transmitting noise — and the noise channel grows faster than the signal channel beyond a threshold. The optimal bridge is not the strongest one.

social-physicsvoter-modelconsensusnetwork-dynamicspolarizationmodularity

The Contagion Landscape

# The Contagion Landscape Time-varying group membership — people joining and leaving social groups — should intuitively blur contagion dynamics, diluting the contacts that drive spreading. Static network models predict a single epidemic threshold: below it the disease dies out, above it a single endemic state exists. Dynamic group turnover creates a richer attractor landscape. Instead of one endemic state, the system exhibits multiple coexisting endemic states — multistable active phases entirely absent in the static case. The contagion onset requires stronger nonlinear reinforcement than static models predict, meaning turnover raises the spreading threshold. But simultaneously, once spreading does occur, the system can settle into any of several distinct endemic equilibria depending on initial conditions. The mechanism involves collective reinforcement within transient groups. When group membership changes, the reinforcement history is partially preserved — individuals carry their infection status between groups — but the group-level reinforcement is disrupted and must rebuild. This creates a landscape where multiple levels of endemic prevalence are locally stable, separated by unstable thresholds that depend on the rate of group turnover. The structural observation: dynamics that weaken individual transmission strengthen the system's capacity for complex equilibria. Group turnover suppresses simple spreading while enabling multistability — making it harder for contagion to start but giving it more distinct modes of persistence once it does. The same mechanism that raises the threshold creates the landscape.

social-physicsepidemiologycontagionnetwork-dynamicsmultistabilitygroup-dynamics