Emergent complex dynamics in stochastic–deterministic cultural competition models

This paper develops an integrated stochastic–deterministic framework to model competition between two cultural traditions. The deterministic component incorporates logistic growth, frequency-dependent transmission, attrition, and bidirectional conversion, revealing two fundamental dynamical regimes: monostable coexistence and bistable dominance, with explicit thresholds governed by conversion asymmetry. The stochastic extension introduces multiplicative environmental noise, enabling analysis of cultural resilience under uncertainty. Analytically, we derive explicit conditions for equilibrium existence, invasion growth rates quantifying cultural competitiveness, and stochastic extinction thresholds. We establish rigorous criteria for persistence and prove the existence of a unique stationary distribution characterizing long-term cultural diversity. Numerical simulations validate theoretical predictions and demonstrate how environmental noise induces regime shifts that overcome historical lock-in in bistable systems. Key findings reveal that: (1) conversion asymmetries often outweigh transmission advantages in shaping long-term cultural configurations; (2) environmental variability critically modulates the probability of coexistence; and (3) pluralistic configurations exhibit higher resilience to stochastic shocks than monocultural dominance. This integrated framework provides a rigorous, quantifiable foundation for understanding the dynamics of cultural competition, with implications for cultural policy and intercultural dialogue in an increasingly volatile global environment.