On the Formation of a Hierarchical Event Representation of Hybrid Time for Simulation of Extreme Threshold Development of Physical Processes
A. Yu. Perevaryukha
Abstract
Abstract Many processes studied in technical physics are associated with abrupt changes in the functioning of the observed system. Such phenomena are, e.g., the onset of destruction of engineering structures or breakdowns of insulating material when a certain deformation or stress threshold is reached. After achieving the threshold level, the system is in a certain transient mode, after which it transits to a new state, possibly, with rapid catastrophic destruction. Simulation of such phenomena has always been particularly difficult, since the space of bifurcation parameters in real situations is multidimensional and is not limited to a phase plane. The solution to the problem may lie in the use of continuous-discrete models with eventfulness and predictive structures—further development of the concept of hybrid systems. The method proposed makes it possible to explicitly form a set of transitions between the states of the simulated system with critical threshold situations. A structure of hierarchical event time for computational modeling of extreme physical processes has been developed on the basis of hybrid automata and a method for redefining equations with a discontinuous right-hand side. The method of forming the hierarchy of events can be applied to the problems of modeling cell activation chains in immunology and the staging of early ontogenesis in the theory of evolution. In the new computational models developed on the basis of the hybrid-event method, chaotic regimes for the trajectory, the phenomenon of intermittency, and standard cycle birth bifurcations can arise.