Russian Federation
Russian Federation
UDC 910.1
UDC 531.3
Methods of studying the stability of natural pasture ecosystems (PE) in the arid zone of Russia, which is subject to degradation and desertification, are considered. The simulation was carried out for PE located in two possible ecological states: in the degradation mode and the other, when the ecosystem is stable. A system of ordinary differential equations (ODES) was used in mathematical modeling. The variants of PE behavior in various functional conditions are considered. The results are discussed in the context of the sustainability of ODE solutions modeling PE. At the same time, it was assumed that the stability of the ODE solutions a priori corresponds to the stability of the PE. New approaches to identifying the stable functioning of PE as a field of stable solutions of differential equations are demonstrated. The stability of the ODE was evaluated by matrix algebra methods, which determine the stability by the values of the eigenvalues of the ODE matrices, the real part of which should be located in the negative region. The second aspect relates to the localization of eigenvalues using Gershgorian circles, which reduces the search area for stable solutions by constructing circles where the eigenvalues of the ODE matrices should be located. It is proposed to use the ODE and the Gershgorin circle method in the tasks of managing pasture ecosystems. The asymptotic stability of ODE and PE solutions is discussed in the context of the ecological dynamics of soil-vegetation plant communities.
mathematical modeling, pasture ecosystems, stability of solutions, differential equations, Gershgorin circles
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