Internal security processes protect all levels of living systems from error and disruption produced by internal and external factors. Such processes allow organizations to survive and evolve in a hostile environment. An internal security subsystem may be present at each level of organization recognized for living systems: cell, organ, organism, group, organization, society, and supranational system. In order for internal security processes to be effective, they must ordinarily maintain steady relationships with the other 19 processes which are critical to living systems (Miller, 1978). Optimal levels of security effectiveness exist which maximize the probability of system success. Too much security results in rigidity so the system cannot evolve or adapt to environmental changes, while too little security results in chaos so the system cannot survive. A catastrophe model can be used to describe the relationships between probability of system success, system health, and effectiveness of security processes.
Useful insights into the representation of natural systems can be gained by decomposing directed graphs (digraphs) into elementary components. Arcs of digraphs can be split into male demiarcs (outarcs) which leave vertices and female demiarcs (inarcs) which enter demiarcs. Likewise, a vertex can be split into an input perceiving side called the creaon and an output generating side called the genon. Digraphs can be regarded as being hierarchically organized because each vertex in a level-l digraph can be expanded into a level-2 digraph. In general, each vertex of a level-i digraph can be expanded into a level-(i+l) digraph. Arcs of a level-i digraph can be regarded as bundles of level-(i + 1) arcs which are split at the vertex boundary. These elementary graphical components are shown to be useful for depicting input-output systems such as organisms, ecosystems and societies.
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