By A. I. Fet, Viktor A. Okhonin
Many folks are interested in crises resulting in mess ups in nature, in social and monetary existence. The booklet bargains a favored account of the causative mechanisms of serious states and breakdown in a huge variety of typical and cultural structures -- which obey an analogous legislation -- and hence makes the reader conscious of the starting place of catastrophic occasions and the how you can stay away from and mitigate their destructive results. The authors practice a unmarried mathematical method of examine the riot of melanoma cells that break residing organisms and inhabitants outbreaks that dissatisfied normal ecosystems, the stability among biosphere and worldwide weather interfered in recent years by way of undefined, the riding mechanisms of marketplace and comparable financial and social phenomena, in addition to the electoral method the right kind use of that is an exhausting accomplishment of democracy
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Additional info for Catastrophes in Nature and Society: Mathematical Modeling of Complex Systems
The phase curves with two equilibrium points are obviously unrealistic: once got to the right of the unstable point, the population would grow infinitely. The same holds true for any even number of equilibrium points. On the other hand, any odd number of equilibrium points would be theoretically possible, though the known populations have no more than three such points. Thus, our classification appears to be exhaustive for the intended biological applications. Note that outbreaks of forest insects acquire specific features in the time of climate change like one we might now witness.
See this relationship in Fig. 4 showing two tumors with the radiuses r1 and r2, where r1 < r2. , the local concentration of cancer cells at the tumor surface is 5/12 at r1 and 5/11 at r2; the correspondence between x and R is univocal in this simplified case. r2 r1 Fig. 4. Local concentration of cancer cells at the tumor surface. Black circles show cancer cells, gray circles show tissue cells. In a general case it can be found as the ratio U1/(U1 + U2), where U1 is the volume of a layer of cancer cells that contacts the interface from inside and U2 is the volume of a layer of tissue cells that contacts the interface from outside.
Note that zero concentration of cancer cells is associated with a nonzero reproduction rate. In this case “reproduction” corresponds rather to spontaneous onset of cancer cells due to various external and internal effects than to the true reproduction by division. These cells are inoffensive because the immune system relatively easily copes with them and kills them before they can reproduce largely enough. The stage when the immune system is able to suppress the proliferation of cancer cells is recorded by the first falling interval of the reproduction curves.