Origin of catastrophe theory

Intellectual movements which have led to the development of catastrophe theory have their origin in philosophy, mathematics and the experimental sciences. The evolution of philosophical views, the progress in the area of non-linear mathematical methods and the development of experimental methods related to the investigation of stability of processes have created favourable conditions for the appearance of catastrophe theory. 

A hypercycle is a more complex organisation form. Its precondition is the presence of several RNA quasi-species which are able to amalgamate chemically with certain proteins (enzymes or their precursors). If such a protein is linked to a quasi-species, the resulting duo favours the replication of a second quasispecies. According to Dyson, the linked populations get stuck in a stable equilibrium. Problems occur at this level Any theory on the origin of replication has the central problem that the replication process must occur perfectly in order to ensure survival . If there are replication errors, these will increase from generation to generation, until the system collapses the error catastrophe has then occurred ... 

Another important motivation for trying to understand the microscopic origins of thermophysical properties is the need for reaUstic safety and risk analysis based on the modeled evolution of hypothetical accidents. This requires, first, solid experimental information on the thermophysical properties, especially the equation of state, up to conditions as far eis practical above the temperatures and pressures of the proposed normal operation. Second, one needs a theory capable of realistically simulating the behavior of specific fluids under truly catastrophic conditions. 

Let s formulate the description of the modem catastrophe theory in the form of interpretation of the dynamic system of emergency situations control. Plotting the theoretical basis of the system within the frame of this theory is defined by original axioms. All the rest statements of the theory are logical conclusions of axioms. In the basis of the axiomatic synthesis of models of catastrophes lies the method of interpretation. Each definition and relation of the system s axiomatic theory is correspondent to some formalized description. 

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