Numerical and Graphical Representations of Allelopathic Effects on Plant Populations: A Mathematical Model Using DDE

Our study aimed to investigate how allelopathic effects impact on plant populations and crop production through a mathematical model. To account for the gradual impact of allelochemicals released by plants, we introduced a delay in the model. We assessed the system's stability using the Routh-Hurwitz theorem, which showed that the system is asymptotically stable when τ < 4.998, but undergoes hopf-bifurcation at τ ≥ 4.998. To examine the sensitivity and directional analysis of the dynamical system, we used the center manifold theory. We presented our findings through numerical and graphical representations generated using MATLAB software.