Mathematical modelling evolutionarily stablebehavior of zooplankton with state constraints

Abstract

The purpose of this work is to create mathematical base and software for solving the problem of finding an evolutionarily stable strategy of zooplankton diel vertical migrations and explaining the observed effects in aquatic ecosystems using this software (in particular, in the northeastern part of the Black Sea). An essential feature of this study is the inclusion in the mathematical model of state constraints on the strategy of behavior, which reflect the vertical limited zone of zooplankton habitat. The presence of state constraints creates the main mathematical difficulties for solving the optimal control problem used in the analysis of the model. The general methodological basis for defining evolutionarily stable behavior is the Darwinian principle "survival of the fittest". However, it remains a problem to construct a mathematical expression for the fitness function of hereditary elements. The efforts of the authors were aimed at creating a software package that allows predicting the evolutionarily stable behavior of zooplankton based on the actual universal extreme principle. The created software package includes, as a main component, a computational module for solving the set optimal control problem with state constraints.