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A decomposition principle for nonlinear dynamic compartmental systems isintroduced in the present paper. This theory is based on the mutually exclusiveand exhaustive, analytical and dynamic, novel system and subsystem partitioningmethodologies. A deterministic mathematical method is developed for the dynamicanalysis of nonlinear compartmental systems based on the proposed theory. Thedynamic method enables tracking the evolution of all initial stocks, externalinputs, and arbitrary intercompartmental flows, as well as the associatedstorages derived from these stocks, inputs, and flows individually andseparately within the system. The transient and the dynamic direct, indirect,acyclic, cycling, and transfer (diact) flows and associated storagestransmitted along a particular flow path or from one compartment--directly orindirectly--to any other are then analytically characterized, systematicallyclassified, and mathematically formulated. Thus, the dynamic influence of onecompartment, in terms of flow and storage transfer, directly or indirectly onany other compartment is ascertained. Consequently, new mathematical systemanalysis tools are formulated as quantitative system indicators. The proposedmathematical method is then applied to various models from literature todemonstrate its efficiency and wide applicability.

Nonlinear Decomposition Principle and Fundamental Matrix Solutions for Dynamic Compartmental Systems