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<p>A mathematical model is framed to examine the growth of competitive plants in the presence of toxicity. It has been noted that presence of toxic compounds changes the structure and activity of soil, which has a negative impact on the growth of mutual competitive plants. A strong, biologically accurate framework for simulating plant competition under toxicity is offered by DDEs. They are crucial for ecological forecasting, conservation biology, and pollution control because they capture growth lags, stability changes, competitive interactions, and delayed toxicity impacts. Both the plant population <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\:{P}_{1}\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\:{P}_{2}\)</EquationSource> </InlineEquation> assume to follow logistic growth. The toxicity does not effect the plant biomass immediately but takes incubation time denoted by delay parameter <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\:\tau\:\)</EquationSource> </InlineEquation>. The positivity and non-zero equilibrium have been calculated. Stability analysis is performed about the equilibrium. The complex behaviour, Hopf bifurcation is observed for the crucial value of the delay parameter <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\:\tau\:\)</EquationSource> </InlineEquation>. Explicit methods are used to determine the direction and stability of bifurcating periodic solutions. Sensitivity analysis is used to determine the sensitivity of solutions of the model when values of parameters are varied. MATLAB is used for simulation.</p>

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Studying the Role of Delay Caused by Toxicty in Two Mutual Competiting Plant Population

  • 期刊论文

  • 发表日期：

    2025年9月2日

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  • Pankaj Kumar,
  • Davneet Kaur

摘要

A mathematical model is framed to examine the growth of competitive plants in the presence of toxicity. It has been noted that presence of toxic compounds changes the structure and activity of soil, which has a negative impact on the growth of mutual competitive plants. A strong, biologically accurate framework for simulating plant competition under toxicity is offered by DDEs. They are crucial for ecological forecasting, conservation biology, and pollution control because they capture growth lags, stability changes, competitive interactions, and delayed toxicity impacts. Both the plant population \(\:{P}_{1}\) and \(\:{P}_{2}\) assume to follow logistic growth. The toxicity does not effect the plant biomass immediately but takes incubation time denoted by delay parameter \(\:\tau\:\) . The positivity and non-zero equilibrium have been calculated. Stability analysis is performed about the equilibrium. The complex behaviour, Hopf bifurcation is observed for the crucial value of the delay parameter \(\:\tau\:\) . Explicit methods are used to determine the direction and stability of bifurcating periodic solutions. Sensitivity analysis is used to determine the sensitivity of solutions of the model when values of parameters are varied. MATLAB is used for simulation.