Bifurcation induced by delay parameter in plant growth dynamics

Kaur, Diljot

doi:10.1088/1742-6596/2267/1/012031

J. Phys.: Conf. Ser.

2022

DOI: 10.1088/1742-6596/2267/1/012031

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Bifurcation induced by delay parameter in plant growth dynamics

Diljot Kaur

Abstract: In this paper, a mathematical model is proposed for plant growth dynamics using delay differential equations. The state variables considered are: plant biomass and nutrient concentration. It is assumed that the delayed nutrient concentration adversely affects the plant growth. The positivity of solutions is established and the feasible interior equilibrium point is calculated. The stability of the system around the interior equilibrium is checked. Hopf-Bifurcation occurred around the critical value of the dela… Show more

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2023

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Determination of Bifurcation Points in the Functioning of “Soil-Plant–air” System

Maksimov

Kalimullin

Alekseev

et al. 2023

Vestnik of Kazan State Agrarian University

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To date, a number of mathematical models of plant growth, developed by domestic and foreign scientists, are known. However, the issues of determining the bifurcation points that arise during the functioning of “soil-plant-air” system have not been sufficiently considered. In relation to the issues considered in the article, the bifurcation point is a critical state of the “plant” subsystem, at which it becomes unstable with respect to fluctuations in natural and climatic conditions (drought, frost, prolonged rains, etc.) and there is uncertainty in the development of plants (further growth or their death), as well as the intensive growth of plants as a result of the corresponding technological operations. For control and operational management of the formation of agricultural crops, it is desirable to know the bifurcation points determined by the biological time of plant growth and extreme weather situations. Therefore, the main goal of research is the analytical determination of bifurcation points observed during the vegetation of plants. The “plant” subsystem at the bifurcation point can be simultaneously in two or more states. As a result of the analysis of the obtained analytical dependences of various possible states of “soil-plant-air” system, it is proposed to subdivide bifurcations into negative and positive ones. A method has been obtained for determining bifurcation points during the functioning of “soil-plant-air” system. Under natural and climatic conditions, critical situations can arise with insufficient incoming substances to “soil-plant-air” system, such as light supply, moisture supply, heat supply, food supply and gas supply of plants. As a result of analytical studies, bifurcation points were determined in “soil-plant-air” system, depending on the radiation balance (R) formed on the underlying surface, slopes of different exposure and steepness, and coefficients characterizing light, moisture, heat, food and gas supply plants.

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Determination of Bifurcation Points in the Functioning of “Soil-Plant–air” System

Maksimov

Kalimullin

Alekseev

et al. 2023

Vestnik of Kazan State Agrarian University

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show abstract

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Bifurcation induced by delay parameter in plant growth dynamics

Cited by 1 publication

References 9 publications

Determination of Bifurcation Points in the Functioning of “Soil-Plant–air” System

Determination of Bifurcation Points in the Functioning of “Soil-Plant–air” System

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