Modeling Governance Constraints in Heterogeneous Multi-Agent Systems: A Dynamical Framework

Modern multi-agent systems (MAS) increasingly operate as autonomous decision-makers under organizational and regulatory constraints, raising questions about how governance shapes collective stability, coordination, and role differentiation. Existing formalisms model cognitive reasoning, computational coordination, or organizational governance largely in isolation, with no dynamical framework treating governance as an intrinsic, state-dependent constraint on agent evolution.

This paper develops such a model. Heterogeneous agent form F evolves under three coupled components — cognitive dynamics, environmental interaction, and a governance constraint field — through dF/dt = G_int(F) + G_env(F, E) + G_ctrl(F, C) on a finite-dimensional smooth submanifold of an underlying Polish form space, with the Polish structure providing a measurable extension for stochastic forms.

Under stated assumptions we establish three results: (i) a governance threshold μ_c at which, under standard Hopf assumptions, a Hopf-type bifurcation can occur in the linearized dynamics; (ii) a stratification property showing that, under weak coupling and spectral separation in the interaction matrix, heterogeneous MAS exhibit hierarchical role differentiation predictable from the dominant spectral components; and (iii) a complexity upper bound C_adapt^max / (λ_s · α) on governance-constrained optimal control, yielding a model-implied indicator of departure from the governance-constrained regime when the bound is exceeded under non-decreasing complexity. We additionally introduce a five-type operational agent taxonomy and a lifecycle finite-state machine. An illustrative five-agent simulation with parameter sweeps and topology comparisons (cyclic, random, scale-free) illustrates qualitative consistency with the three predictions in the small-scale regime; comprehensive validation on larger MAS is future work. Explicit falsifiability conditions are stated.