Modeling of a Crisis in the Biophysical Process by the Method of Predicative Hybrid Structures

Abstract

Crisis processes of biosystems often develop according to scenarios of rapid collapse, which cannot be predicted by statistical methods. This paper develops a method for constructing hybrid computational models using event-hierarchy representation for biophysical processes. System events calculated by the algorithm change the order of calculation of equations according to a given set of rules. The rules of physically conditioned redefinition of the right-hand sides of differential equations are used. The predicates employ the calculations of a group of accompanying characteristics, which are an integral part of the controlled biophysical dynamics. The model is investigated by presenting a computational scenario with a set of parameters, initial values, and an algorithm for making decisions about changing the impact for discrete time. Using computational experiments, a real outcome scenario for a situation that leads to the collapse of a biophysical system at a controlled level of exposure is described. The scenario sets the logic for making control decisions to change the level of external pressure on the natural environment. It is shown as a result of modeling that the transition of the process to an oscillatory mode leads to the choice of a risky control mode. It has been established that the dynamics of many real water populations has a point of threshold reduction in the efficiency of replenishment of stocks. The model scenario uses transformations of the phase portrait of iterations, which, in the presence of disconnected boundaries of the areas of attraction of alternative attractors and a strange chaotic repeller, lead to the uncertainty effects arising due to chaotic modes in a deterministic model. The properties of the described model scenario with a chaotic regime of dynamics are confirmed by the example of the catch of oceanic species of crustaceans.