Table 1.
Structural comparison of the HK model, the Deffuant Relative Agreement (RA) model, and the opinion update mechanism of the model proposed in this study. This opinion component follows the pairwise random interaction structure of the Deffuant approach with a fixed global confidence threshold, applied on an explicit network topology and conditioned on agents’ adoption statuses. The integer attitude scale [1, 100] is a uniform discretization of [0, 1] (step size = 0.01) and is mathematically equivalent to the continuous-space Deffuant formulation.
Fig 1.
Schematic diagram of the adoption threshold model used in this study.
Black-framed circles indicate not-yet-adopted neighboring agents, red-framed circles already-adopted neighboring agents. Andy makes his decision based on the actions of his neighboring agents. (a) One of Andy’s three neighbors has acted, thus meeting the required 0.3 adoption threshold. (b) In this case Andy has four neighbors, of which only one has adopted the product, therefore the 0.3 adoption threshold is not met.
Table 2.
BCAT model and simulation system parameters.
Fig 2.
Graphical user interface of the Python 3 BCAT simulation.
Parameter setting area is along the left side. Upper right: attitude, threshold, and degree distribution plots. Middle right: network agent attitude trajectory over time. Pink, red, orange, brown, yellow, green, lime, turquoise, cyan, sky, blue, violet, magenta and black colors indicate low-to-high agent numbers. Lower right: adoption dynamics (red S-shaped curve represents cumulative adoption over time, green inverse S-curve cumulative non-adoption over time) and new adopter dynamics (orange bell-shaped curve). Lower left: social network structure arranged in a two-dimensional grid. Red node represents already-adopted agent, green not-yet-adopted agent. Darker color indicates higher attitude value.
Fig 3.
Simulation process flowchart for proposed BCAT model.
Simulation process time complexity is O(NT), where N and T respectively represent the number of agents and number of simulation time steps.
Fig 4.
Simulation result illustrating favorable review and good sales scenario.
Fig 5.
Simulation result illustrating favorable review but poor sales scenario.
Fig 6.
Two simulation runs with identical parameter settings but different processes and results: (a) favorable review and good sales scenario, (b) favorable review but poor sales scenario.
Table 3.
Results from statistical analysis of primary model-related parameters. For Feature Importance entries, the standard error of per-tree importance estimates is ≤0.001 for all entries (100-tree Random Forest ensemble, N > 15,000 per network topology); the remaining four methods produce deterministic analytical results, so standard errors are not applicable. Parameter Importance values (Pearson correlations) closely approximate Standardized Regression coefficients because the five input parameters are varied independently in the sensitivity analysis design, making them approximately uncorrelated; under orthogonal predictors, the two measures are mathematically equivalent. All avg-of-thresholds values are stored as integers in [1, 100] and are equivalent to fractional adoption thresholds in [0.01, 1.00] via the conversion , as implemented in the adoption decision rule of Algorithm 3; the sensitivity analysis sweeps avg-of-thresholds across the range [10, 70], corresponding to fractional thresholds of [0.10, 0.70].
Fig 7.
Correlation coefficient heatmaps showing various primary model-related parameters and good sales indicator (GSI) values across four network types: (a) regular lattice, (b) small-world, (c) random and (d) scale-free.
Fig 8.
Sensitivity analysis results for various primary model-related parameters and good sales indicator (GSI) values across four network types (regular lattice, small-world, random and scale-free).
(a, b) bounded-confidence, (c, d) avg-of-attitudes, (e, f) std-of-attitudes, (g, h) avg-of-thresholds, (i, j) std-of-thresholds. Left plots show results grouped by network type; right plots show aggregated results across all networks.
Fig 9.
Statistical analysis results for primary BCAT model parameters.
(a, b) feature importance, (c, d) multivariate regression, (e, f) partial correlation, (g, h) standardized regression, (i, j) parameter importance. Left plots: experiment data are grouped according to network type for statistical analysis. Red bar represents regular lattice, yellow bar small-world, green bar random, and blue bar scale-free networks. Right plots: statistical analysis results for entire body of experimental data.
Fig 10.
Mechanism decomposition on the regular lattice.
(a) MD-A isolates the coordination failure channel: FRI = 1.0 by construction, and GSI declines sharply between avg-of-thresholds = 30 (GSI = 0.976) and 40 (GSI = 0.026), indicating a phase transition in coordination dynamics. (b) MD-C decomposes the total adoption gap (1 − GSI) into opinion clustering (1 − FRI, red) and coordination failure (FRI − GSI, blue). The opinion clustering contribution is negligible because the user-friendly testimony effect (Algorithm 3, Scenarios 1.1 and 2.2) restores FRI to approximately 1.0 even though MD-B alone yields FRI = 0.600 (dotted line). N = 400 agents, 1,000 runs per point.
Fig 11.
BCAT model configured as a bounded confidence-based opinion dynamics model (adoption dynamics removed).
Adoption thresholds are unattainable (avg-of-thresholds = 100, std-of-thresholds = 0) and initial adopters are absent (no-of-pioneers = 0), ensuring a complete model focus on opinion dynamics. Opinions evolve under the influence of a bounded confidence mechanism (bounded-confidence = 10) with a convergence rate of 0.4. The network is a regular lattice generated with a rewiring probability of 0.00. Each of the 400 agents is connected to an average of 8 neighbors. As shown in attitudes trajectory and distribution data, agent attitudes were clustered over 300 time ticks, thus highlighting the bounded confidence effect on opinion clustering in a structured network.
Fig 12.
BCAT model configured as an adoption threshold model, with opinion dynamics removed by uniform agent attitude parameters (avg-of-attitudes = 100, std-of-attitudes = 0).
Simulation consists of a regular lattice network structure with 400 agents and 1600 edges, with each agent connected to an average of 8 neighbors. Adoption process is governed by threshold distribution (avg-of-thresholds = 20, std-of-thresholds = 10). Results indicate complete adoption by all agents within 50 time ticks, highlighting the influence of critical mass, network structure, and threshold heterogeneity on innovation diffusion.