Fig. 7.13. Dynamics of the utilisation coefficient (h = N/A) for three different dynamic regimes: (a) regular regime without oscillations (A = 5), (b) doubling oscillations (A = 9.447), (c) chaos (A = 36.5). The total biomass and the total amount of matter are measured in dimensionless units.
chaotic behaviour of species biomasses. The chaos is especially annoying because of the basic unpredictability of drastic changes in the ecosystem state. Let us compare the two pictures showing the dynamics of eex(t) and h(0 (Figs. 7.12c and 7.13c). The peaks of ex and falls of h, although occurring simultaneously, are irregular. Although at these times the fish biomass increases sharply (the ex is sharply increasing) the increase is of a short duration. At the same time the degree of utilisation falls sharply by almost half (see Fig. 7.13c). In the second experiment we vary only the coefficient a0 = a at the fixed total amount of matter, A = 36.5. The qualitative dynamics of the system is similar to that obtained in the previous experiment. As the value of a increases the system passes through the regular regime without oscillations (the corresponding a-interval is very short; even for a = 0.01 long-periodic oscillations arise). In contrast to the previous case the pre-stochasticity regime is relatively long: it corresponds approximately to the interval a [ [0.1,0.3]. At last, a state of chaos arises beginning with a < 0.33. However, the results which were obtained for the dependencies of ex and h and shown in Figs. 7.14b and 7.15b differ from the previous ones, especially for the specific mean exergy. If the utilisation coefficient reaches its saturation at approximately a = 0.035 when the oscillations already dominate in the dynamics of the ecosystem (that, in general, coincides with the previous case), then the specific mean exergy attains its maximum just when the pre-stochastical regime arises. Just after this, the value of ex begins to decrease very slowly. The change of dynamic regimes is very weakly
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