Generalized Morphogenesis Theory: A Flow-Inertia Modeling Framework for Cross-Scale Dynamics of Dissipative Structures

Abstract

Understanding structural similarities across dynamical systems at different scales remains a central problem in nonlinear science [1, 3]. Here we propose a modeling framework for cross-scale morphogenetic dynamics, termed Generalized Morphogenesis Theory (GMT), based on a flow-inertia formulation: O_FD O_INLINEFIG[Formula 1]C_INLINEFIGM_FD(1)C_FD where S denotes system state, E environmental input, F (E, S) a driving function, and {micro}(S) an inertia function representing resistance to change. This formulation provides a structural representation that encompasses several classical dynamical models--including Newtonian relaxation, logistic growth, and reaction-diffusion systems [13]--under appropriate parameterizations. Non-dimensionalization reveals a small set of control parameters governing regime transitions. Empirical validation is performed across two independent scales. At the organism scale, crop growth time-series datasets from multiple species exhibit consistent multiplicative dynamics F (E, S) = f (E) {middle dot} S, statistically preferred over additive alternatives in 5 of 6 independently tested systems ({Delta}AIC ranging from +2 to +891; R2 up to 0.98). Independently estimated inertia time constants agree in two plant systems (cucumber:{tau} = 3.7 days, CV=3.3%; maize:{tau} = 36.8 days, CV=17.3%), with the 10-fold ratio consistent with structural complexity differences. At the molecular scale, publicly available perturbation transcriptomics datasets (Perturb-seq) show directional response structures consistent with the proposed flow-inertia decomposition (93% causal direction agreement across three independent datasets; p < 10-25). Across domains, recurrent dynamical motifs are organized into 12 canonical design patterns, derived from a 2 x 2 x 3 orthogonal structure (4 elementary operations x 3 temporal scales), associated with stability classes and bifurcation conditions. These results suggest that the flow-inertia formulation functions as a domain-independent structural modeling principle for dissipative morphogenesis.