Convergence of Automatic Operations to Controlled Operations via Internal Capacity Building

Abstract

Despite the extensive literature on dual-process theories of cognition, there remains limited understanding of how automatic operations (System 1) can converge toward controlled operations (System 2) over time, and under what conditions such alignment improves individuals’ quality of life. This study addresses this gap by developing a nonlinear dynamic model of automatic-controlled system interaction, drawing on expectancy-disconfirmation theory and behavioral frameworks such as prospect theory. Methodologically, we formulate a first-order nonlinear difference equation to capture the updating of automatic processes based on discrepancies with controlled goals. Using stability analysis, we identify conditions under which individuals’ automatic operations converge to their controlled operations, and when they instead exhibit cyclical or unstable patterns. To extend the model, we incorporate an internal capacity building (or “internal work”) parameter that reflects practices such as mindfulness, boundary setting, and present-moment awareness. Our analytical results reveal significant heterogeneity: some individuals naturally achieve convergence, while others require internal work to reach stable alignment. Increasing internal work expands the proportion of individuals whose automatic operations converge with their controlled system, effectively shifting cognitive processing toward greater deliberation. The implications are twofold. Theoretically, this research contributes a mathematical framework for linking internal psychological processes with dual-system models of cognition. Practically, it highlights the potential of capacity-building interventions—such as mindfulness-based practices—to foster self-alignment, enhance autonomy in decision-making, and improve overall well-being.