Use of Systems Theory, Directed Graphs, and Pulse Process Models in an Adaptive Approach to Agroecosystem Health and Sustainability - Integrated Assessment of Health and Sustainability of Agroecosystems - page 105

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fIGuRe 4.3 Oscillating impacts of knowledge at vertices 6 (agrochemical use) and 7 (cof-
fee production) in a pulse process analysis of Githima digraph.

sensitive to increase in the weight of at least one arc in the digraph (Table 4.5). Of the
28 impacts that are not sensitive to increases in the weight of arcs, only 8 are indirect
and nonambivalent. The ambivalent impacts of soil fertility on vertices 12, 27, and 31
stabilize as a result of increases in the weights of some of the arcs in the digraph.
The digraph consists of two main (with more than two vertices) strong compo-
nents. The first strong component comprises vertices 3, 4, 7, 8, and 13 linked by two
positive- and one negative-feedback loops. The second consists of vertices 6, 11, 12,
14, 15, 16, 27, 28, and 31 joined into 15 feedback loops, 3 of which are negative. The
first strong component is pulse stable. Inverting any one of arcs [3, 7], [4, 3], and
[7, 13] makes this strong component value stable under all simple autonomous pulse
processes. The second strong component is unstable. Among the simplest strategies
that produce value stability are (1) removal of arc [11, 16] accompanied by inversion of
arc [15, 11] and (2) removal of arc [14, 11] accompanied by inversion of arc [15, 11].