Resonant Bifurcation in Cognitive Systems: A Model of Transitions Between Stable States

Preface This paper is the twelfth contribution in the Resonance Architecture series, which develops a unified dynamical framework for understanding language, meaning, and cognition as emergent properties of resonant processes in complex systems. Earlier works in the series established: resonance as a primary mechanism of coordination, stabilization as the formation of attractors, discretization as the emergence of symbolic and linguistic structures, across physical, biological, cognitive, and artificial domains. While previous articles focused on stable resonant architectures, the present work addresses a complementary and necessary aspect: transitions between stability regimes. Real cognitive systems do not remain indefinitely within a single attractor. Instead, they undergo critical reorganizations in response to changing constraints, internal variability, and accumulated history. This paper introduces the concept of resonant bifurcation as a general mechanism by which cognitive systems reorganize their internal geometry, giving rise to multiple alternative stable modes of functioning. Rather than interpreting such transitions as failures or breakdowns, we treat them as structurally lawful phase transitions intrinsic to resonant architectures. By formalizing these transitions, the present work completes an essential part of the resonance-based framework, extending it from static stability to dynamic transformation.