Affiliation:
1. Tyumen State University, V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences
2. Tyumen State University, Derzhavin Tambov State University
Abstract
In this paper we constructed a mathematical model based on a continuous dynamic system, which is formalizing the interaction of fusarium fungi, wheat plants and soil microorganisms (mycophages and saprophages). The paper presents a statistical analysis of the available experimental data obtained under laboratory conditions, on the basis of which we solved the problem of restoring biologically interpreted parameters of the constructed model of the considered ecological system. The paper also considers the problem of impulse control within the constructed mathematical framework, which corresponds to a correction on the food webs in the system in order to stimulate the growth of the populations of natural antagonists of the fusarium fungus causing wheat pathology by applying special mixtures of organic fertilizers to the soil. We obtained conditions that guarantee controllability within the framework of the constructed mathematical model, as well as providing continuous dependence of solutions of the modeling equations on control.
Publisher
Tambov State University - G.R. Derzhavin
Reference10 articles.
1. [1] G.S. Abawi, J.W. Lorbeer, “Several aspects of the ecology and pathology of Fusarium oxysporum f. sp. cepae”, Phytopathology, 62 (1972), 870–876.
2. [2] J.J. Marois, D.J. Mitchell, “Effects of fungal communities on the pathogenic and saprophytic activities of Fusarium oxysporum f. sp. radicis-lycopersici”, Phytopathology, 71 (1981), 1251–1256.
3. [3] S.N. Smith, “An overview of ecological and habitat aspects in the genus Fusarium with special emphasis on the soil-borne pathogenic forms”, Plant Pathology Bulletin, 16 (2007), 97–120.
4. [4] G. Innocenti, M.A. Sabatini, “Collembola and plant pathogenic, antagonistic and arbuscular mycorrhizal fungi: a review”, Bulletin of Insectology, 71:1 (2018), 71–76.
5. [5] F. Meyer-Wolfarth, S. Schrader, E. Oldenburg, J. Weinert, F. Brunotte, “Collembolans and soil nematodes as biological regulators of the plant pathogen Fusarium culmorum”, Journal of Plant Diseases and Protection, 124 (2007), 493–498.