The DPA Framework: A Structural Diagnostic for Resonant Propensity in Complex Systems

Across multiple complex systems, a recognizable pattern recurs: coherent, self-sustaining dynamics that persist within bounds, degrade predictably under stress, and resist simple cross domain description. Despite this recurrence, no minimal structural language exists for diagnosing when such behavior is possible.

Such patterns can arise when three structural conditions are satisfied: dimensional freedom (D), proportional distribution (P), and alignment (A). Together these constitute a diagnostic for Resonant Propensity (R) – the conditional tendency for a system to develop and sustain bounded, self-reinforcing dynamics through internal feedback.

The structural relationship R ∝ D × P × A indicates that resonant propensity depends on the simultaneous presence of D, P, and A, and collapses when any enabling condition fails. Propensity is therefore not inherent to any architecture but emerges only when these conditions are jointly satisfied.

The framework stratifies dynamical regimes from rigid order through chaotic instability to resonant propensity, and suggests structural analogues for the recurring failure modes observed across domains, including vanishing gradients in neural networks, trophic cascades in ecology, misaligned incentives in organizations, decoherence in quantum systems, and phase mismatch in physics.

DPA does not compete with domain-specific models, nor does it define resonance itself. Instead, it identifies the structural conditions enabling a system to enter and sustain resonant regimes, and provides a framework to diagnose systemic instability and the specific threshold for collapse.

Keywords: resonance, resonant propensity, complex systems, dimensional freedom, proportional distribution, feedback alignment, structural conditions, multiplicative dynamics, self-correction, dynamical systems, neural networks, cross-domain framework

Publication date: 2026-02-28