  This article develops a new mathematical method for holistic analysis of
nonlinear dynamic compartmental systems through the system decomposition
theory. The method is based on the novel dynamic system and subsystem
partitioning methodologies through which compartmental systems are decomposed
to the utmost level. The dynamic system and subsystem partitioning enable
tracking the evolution of the initial stocks, environmental inputs, and
intercompartmental system flows, as well as the associated storages derived
from these stocks, inputs, and flows individually and separately within the
system. Moreover, the transient and the dynamic direct, indirect, acyclic,
cycling, and transfer (diact) flows and associated storages transmitted along a
given flow path or from one compartment, directly or indirectly, to any other
are analytically characterized, systematically classified, and mathematically
formulated. Further, the article develops a dynamic technique based on the
diact transactions for the quantitative classification of interspecific
interactions and the determination of their strength within food webs. Major
concepts and quantities of the current static network analyses are also
extended to nonlinear dynamic settings and integrated with the proposed dynamic
measures and indices within the proposed unifying mathematical framework.
Therefore, the proposed methodology enables a holistic view and analysis of
ecological systems. We consider that this methodology brings a novel complex
system theory to the service of urgent and challenging environmental problems
of the day and has the potential to lead the way to a more formalistic
ecological science.

Systems and Control;Systems and Control;Dynamical Systems;Optimization and Control;Quantitative Methods