Scenario Modeling of the Collapse of Red King Crab Stocks under the Expert Control of the Annual Catch

For a number of actual situations, when the impact management strategy is determined based on the decisions of experts and stakeholders, it is advisable to carry out the modeling of biosystems in the form of a set of scenario computational experiments. The scenario approach allows us to compare development for a situation given by formal conditions, while simulating the logic of expert decisions and assessing the consequences for biological resources. In the structure of the scenario model, it is necessary to include conditions for changing the nature of the process, changing the behavior of the system, and defining a new control action. It is proposed to use a special form of representation of the model time with continuous intervals and a hierarchy of events, which corresponds to the considered biological problem. The model with the property of multistability is formed based on the equations for the formation of adult generations. These equations change depending on the current stages of development and reproduction conditions of crabs. The dynamics of the situation that led to the collapse of red king crab (Paralithodes camtschaticus), also called Kamchatka crab, stocks due to irrational fishing is considered. The scenario develops from stages with sharp aperiodic population fluctuations, which are reflected by a transient chaotic regime. The discrete component of the trajectory of the model with hybrid time and formalized expert control logic of expert fishery management describes the moment of the population’s collapse as the loss of the invariance property by the attractor, which is in contact with the boundary of its basin of attraction.