Abstract
A two-compartment mathematical model is proposed for the study of individual plant growth dynamics with time lag due to the presence of toxic metals in the soil. It is assumed in the model that nutrient uptake by the roots is hindered by the presence of the toxic metals. It is further assumed that there is less transfer of nutrients from the root compartment to the shoot compartment due to the toxic metals. However, the nutrient concentration decreases in the root compartment as well as in the shoot compartment, resulting in a decrease of the structural dry weight of the roots and shoots respectively. This effect was studied by considering time lag in the utilization coefficient of the nutrient concentration in the roots in the presence of toxic metals. It is further assumed in the model that the nutrient use efficiency is also affected by the presence of toxic metals, resulting in a decrease of the structural dry weight of the shoots. The inclusion of time lag results in the disturbance of the interior equilibrium stability and Hopf bifurcation occurs for a critical value of the delay parameter. This entire phenomenon was captured by numerical simulation.
Abstract from the paper’s OpenAlex record; open copy licensed cc-by-nd. Read at the source ↗
The text the model read, with the source record’s inline markup (italics, sub- and superscripts) rendered and its character entities decoded; quote offsets refer to the raw text.
Claims 5
Claim · model-written summary
Toxic metals reduce modeled root nutrient concentration and structural dry weight.
Not reportedTaxonTreatmentComparator
Verbatim
e0“nutrient concentration decreases in the root compartment as well as in the shoot compartment, resulting in a decrease of the structural dry weight of the roots and shoots respectively”
Claim · model-written summary
Modeled shoot nutrient concentration decreases in the presence of toxic metals.
Not reportedTaxonTreatmentComparator
Verbatim
e0“nutrient concentration decreases in the root compartment as well as in the shoot compartment”
Claim · model-written summary
Modeled root structural dry weight decreases.
Not reportedTaxonTreatmentComparator
Verbatim
e0“a decrease of the structural dry weight of the roots and shoots respectively”
Claim · model-written summary
Modeled shoot structural dry weight decreases.
Not reportedTaxonTreatmentComparator
Verbatim
e0“resulting in a decrease of the structural dry weight of the shoots”
Claim · model-written summary
Time lag disturbs interior equilibrium stability and leads to Hopf bifurcation at a critical delay.
Not reportedComparator
Verbatim
e0“The inclusion of time lag results in the disturbance of the interior equilibrium stability and Hopf bifurcation occurs for a critical value of the delay parameter”