Investigating the role of allelochemicals in plant population dynamics via the stability analyses, equilibrium point and Hopf-bifurcation: a delay-differential model

Allelochemicals are chemical compounds produced by plants that can have both positive and negative effects on the growth and survival of other plants in the same population. They are important components of interplant interactions and play a significant role in maintaining the diversity and stability of plant populations. We have taken three plant populations (Formula presented.) in the proposed mathematical model. The interactions between (Formula presented.) plant populations respectively, and (Formula presented.) plant population release allelochemicals and affect the (Formula presented.) plant population. Delay is introduced into the (Formula presented.) plant population to examine the allelopathic effect. The stability is analyzed at a non-zero equilibrium point using the Routh–Hurwitz criteria. Hopf-bifurcation is observed when the delay parameter crosses the threshold value. A similar study of these chemical compounds is possible by using graph theoretical and combinatorial results. So-called topological graph indices are used to study the properties of these chemical structures in many ways. MATLAB is used to draw the dynamic system. Additionally, this research paper plays a significance in climate change.