Modelling the stimulatory and inhibitory allelopathic effects on competing plant populations

The analysis of mutual competition of the growth of plant with particular emphasis on time reliant variations in their densities has been done in our present work. We are proposing a mathematical model of plant population growth with competitive and allelopathic impacts that are stimulating as well as inhibitory on each other. Equilibrium points are calculated and stability analysis is performed about non-zero equilibrium point. Delay parameter destabilizes the system when allelopathic effect is supposed to be of stimulatory in nature. The system shows asymptotic stability when delay parameter having value below the critical point. Hopf bifurcation is observed when the value of delay parameter crosses the critical point. The numerical results are substantiated using MATLAB.