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Bounded-confidence opinion models with random-time interactions
1University of Massachusetts Amherst, Department of Mathematics and Statistics, Amherst, Massachusetts 01003, USA.
Physical Review. E
|April 18, 2026
Summary
This study introduces random-time interactions into bounded-confidence models (BCMs) for opinion dynamics. Findings show that inter-event-time distributions significantly impact model behavior, especially for non-Markovian processes.
Area of Science:
- Social dynamics
- Complex systems
- Statistical physics
Background:
- Opinion dynamics models simulate how agents change beliefs through interaction.
- Bounded-confidence models (BCMs) assume agents compromise opinions if sufficiently similar.
- Existing BCM research often assumes deterministic interaction times, ignoring social randomness.
Purpose of the Study:
- To incorporate random-time interactions into BCMs using renewal processes.
- To analyze the impact of inter-event-time distributions (ITDs) on BCM dynamics.
- To compare random-time BCMs with deterministic-time BCMs.
Main Methods:
- Utilized renewal processes to model random social interaction event times.
- Derived approximate governing equations for time-dependent BCM expectations.
- Numerically examined transient and steady-state dynamics on various networks.
Main Results:
- BCMs with Markovian ITDs exhibit consistent statistical properties with the same mean ITD.
- BCMs with non-Markovian ITDs show behavior dependent on ITD type, even with identical means.
- Identified quantitative impacts of ITDs on transient dynamics and convergence.
Conclusions:
- Random-time interactions are crucial for realistic opinion dynamics modeling.
- The choice of inter-event-time distribution significantly influences opinion convergence and stability.
- Future research should consider diverse ITDs for comprehensive BCM analysis.
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