Investigation of stability and oscillatory behavior of allelochemical influence on plants in time delay differential equation model

Mine  Babaoglu; Dipesh; Pankaj Kumar

doi:10.65112/tcmis.10013

Authors

Mine Babaoglu Department of Mathematics and Science Education, Faculty of Education, Kahramanmaraş Sütçü İmam University, Kahramanmaraş, Türkiye https://orcid.org/0000-0003-0819-1166
Dipesh Department of Mathematics, SR University, Warangal-506371, Telangana, India https://orcid.org/0000-0003-4883-9369
Pankaj Kumar Department of Mathematics, Lovely Professional University, Phagwara, Punjab-144411, India https://orcid.org/0000-0002-8289-1868

DOI:

https://doi.org/10.65112/tcmis.10013

Keywords:

Allelochemical, plant response, stability, delay parameter, hopf-bifurcation, time delay differential equation

Abstract

The utilizing of bioassay techniques is common for examining how allelochemicals affect plant processes. In general, at higher allelochemical concentrations, processes are impeded, whereas at lower ones, they are boosted. A mathematical model is developed to analyse this kind of reaction. It is assumed that the response of the plant organism is proportional to the allelochemical dose. This plant response is studied for delayed allelochemical dose using time delay differential equation. The feasible non-zero equilibrium point is examined and the stability analysis is studied about the equilibrium point. The system is stable if the delay in allelochemical dose does not cross a fixed critical value. However, the system exhibits limit cycles via Hopf-bifurcation when delay parameter crosses the fixed critical value. Furthermore, in the situation that the diffusion coefficient transpires. Additionally, it exists within the event exhibiting the diffusion coefficient. Analytical results are supported by MATLAB.

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