Methodology of the Construction of Computational Scenarios for Modeling Extreme States in Living Systems

Abstract

Abstract: We consider a methodology for organizing hybrid computing structures to simulate abrupt changes in controlled natural processes and analyzing phases of extreme environmental phenomena. Systems of differential equations with the dynamically redefinable right-hand side at special moments (events) are used. The truth conditions for transitions are obtained from computing other equations for additional characteristics of the state of a generation. Threshold states in process modeling are the result of the inclusion of trigger functions. Their values on the right-hand side are specifically different from the neutral value only in narrow ranges of the space of changing characteristics of a hybrid system and depend on the initial conditions. The restricted limits of functions and their domain of values rest on the core of the threshold effects for the simulated biosystem, which are observed under special conditions. The method allows us to implement actual qualitative changes in management scenarios as bifurcations of the appearance (reduction) of equilibrium states or the boundary crisis of a complex attractor consisting of intervals scattered in a limited area. Computational scenarios for different population processes are investigated. The collapse of fish stocks is described in the model by the examples of cod in the North Atlantic and sturgeon in the Caspian Sea. The rapid outbreak of their abundance is modeled according to observations on the pulsation of the population size of pests of relict evergreen forests. The threshold scenario of the outbreak of insects in the scenario ends spontaneously due to the local exhaustion of forest resources with a sharp transition to fluctuations of the pest, which are ordinary for the environment. The methodology of organizing the structure for the population model is summarized to predict a wide range of extreme processes related to rapid changes in controlled biological systems and the spread of unwanted biological invasions.