Emergence of Collective Knowledge-Creation Cycles through a Hopf Bifurcation: A Nonlinear Dynamical Formalization of the SECI Model

Nonaka’s SECI model — Socialization, Externalization, Combination, Internalization — isthe most widely adopted framework for organizational knowledge creation, yet it remainsa qualitative spiral metaphor with no closed-form dynamical model. Nonaka himself citedPrigogine’s dissipative structures and Haken’s synergetics, but never wrote equations. Weconstruct a minimal four-dimensional ordinary differential equation system in which the SECImodes interact through cyclic nonlinear coupling — three facilitatory links and one inhibitorylink (𝐼 → 𝑆), derived as the singular limit of a two-timescale model that separates fast re-source competition from slow knowledge enrichment — and show that this signed-loop struc-ture generically produces a Hopf instability; for the sigmoid nonlinearity studied here, the bi-furcation is supercritical. Center-manifold reduction yields a Stuart–Landau equation whoseamplitude measures the strength of self-organized knowledge-creation order — distinct fromaccumulated knowledge, which is modeled as a separate stock variable — and whose phasetracks position in the SECI cycle. The onset condition provides a mathematically precise cri-terion for when episodic knowledge activities coalesce into a self-sustaining creative process.Extending the model to 𝑁 coupled agents with heterogeneous parameters, we demonstratea second critical transition: individual knowledge-creation activity does not imply collectiveorganizational coherence. Team-level order emerges only when inter-agent coupling exceedsits own threshold, partitioning the parameter space into three regimes — inactive, active butincoherent, and collectively organized. Numerical experiments confirm the predicted criticalscaling, identify early-warning signals near the onset threshold, and demonstrate robustnessacross network topologies. These results provide the first closed dynamical-systems formal-ization of SECI, a bifurcation-theoretic mechanism for the emergence of knowledge-creationcycles, and a micro-to-macro account of collective organizational order.