APPLICATION OF PREDICATIVE-REDEFINABLE STRUCTURES FOR MODELING A VARIATIVE DEVELOPMENT OF BIOLOGICAL PROCESSES

Abstract

In the article we considered a new original method of organizing hybrid computing structures for simulating abrupt changes in controlled natural processes and analyzing extreme environmental phenomena. Our Method uses systems of differential equations on adjacent intervals of hybrid time with a dynamically redefined right-hand side at special moments – events. Transition conditions for such events are obtained by calculating the equations for additional characteristics. Threshold states in the dynamics of the process become a consequence of the inclusion of trigger functions. Their values on the right-hand side specifically differ from neutral only in narrow space ranges of the changing characteristics of the hybrid system, for example, initial conditions. The limits of the functions and their range of values proceed from the essence of the nonlinear effects of the biosystem we are modeling under this effect. The approach allows realizing current qualitative changes in control scenarios – such as bifurcations or the boundary crisis of an attractor. The author has investigated computational scenarios for such different processes as the collapse of fish stocks in the case of the Northern Atlantic cod and rapid outbreak of the forest pests in Australia. The outbreak of insects in the hybrid model ends spontaneously with the threshold for the exhaustion of forest resources, with a transition to ordinary for the environent fluctuations of the pest. The practical novelty of our modeling of the outbreak of pests is that extreme phenomenon in the script ends spontaneously according to the internal logic of the process. In this method, we do not need to include a change in parameters from external factors that causes a stop in reproductive activity. Similarly, the epidemic of viruses ends in the formation of collective immunity. The functions of the trigger action will allow targeted bifurcation and change the position of the extremes of dependence. The method is successfully applied to the analysis of situations of collapse of biological resources – quick and unexpected degradation of fish stocks for specialists, which is not replaced by restoration contrary to statistical forecasts. The technique is further generalized to describe a wide range of extreme processes with changes in biological systems.