The model of the dynamics of number of arachnids in the spectrum of their interspecies competitive relationships

The article deals with the construction and research of a mathematical model for studying the dynamics of the number of arachnids herpetobionts in the spectrum of their trophic competitive relations. The problems of determining the necessary variables and calculation coefficients for constructing and studying the model in relation to various trophic situations are discussed. The basis for the model was the nonlinear differential equation of Lotka–Volterra. The studies carried out with the aid of the constructed model have shown that the response of the system to any perturbation is of an oscillatory nature. The nature of the solutions depends on the initial perturbation, and differ in magnitude of the amplitude and period of the oscillations. The steady-state solutions of the mathematical model are multi-period oscillations, which are characteristic for biological systems. Numerical and graphically presented data of the research results of the proposed model are presented.