Advances in Computational Methods and Modeling for Science and Engineering

Mutual competition has an impact on plant population dynamics. There is no indication that this biological phenomenon has a detrimental impact on a plant species' long-term survival. This dynamical phenomenon that affects population dynamics has significant implications for population stability. In this work, the effect of allelochemicals on plant population using competing mathematical model with the help of delay differential equation is studied, and the equilibrium point is calculated. To analyze the impact of allelochemical, delay is introduced and stability is measured. We observe that, when the value of delay parameter, system shows asymptotically stability and when, systems show Hopf bifuraction. The local and global stability analysis about the nonzero equilibrium point is performed using Routh–Hurwitz criteria and Benedixon–Dulac criterion, respectively. Further, we examine the directional analysis of competing plant populations. With this proposed mathematical model, the effects of allelochemicals can better be controlled and further plant growth enhanced.