Model of the Dynamics of the Number of Arachnids in the Spectrum of Their Interspecies Competitive Relationships

Abstract

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 model is based on the nonlinear differential equation of Lotka-Volterra. The studies carried out with the aid of the constructed model show 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 they differ in the magnitude of the amplitude and period of the oscillations. The steady-state solutions of the mathematical model are multiperiod oscillations, which are characteristic for biological systems. The numerical and graphically presented data of the research results of the proposed model are presented.