The study of dynamical interactions between two competing plant populations under the influence of allelochemicals is a current area of active research. In this paper, we have studied the effect of allelochemicals on the plant populations of two competing species model with particular emphasis on time reliant variations in their densities. Positivity, Boundedness, Equilibrium point is calculated. We have also studied the stability of the dynamics system about non-zero equilibrium point with the help of Routh-Hurwitz theorem. The system shows asymptotic stability when the value of delay parameter is less than the critical value. Hopf-bifurcation occurs when the value of delay parameter is greater than the critical value. In additional, we calculate the sensitivity analysis of the dynamics system to understand, how the various source of uncertainty in a model contributes the overall uncertainty.
The study of dynamical interactions between two competing plant populations under the influence of allelochemicals is a current area of active research. In this paper, we have studied the effect of allelochemicals on the plant populations of two competing species model with particular emphasis on time reliant variations in their densities. Positivity, Boundedness, Equilibrium point is calculated. We have also studied the stability of the dynamics system about non-zero equilibrium point with the help of Routh-Hurwitz theorem. The system shows asymptotic stability when the value of delay parameter is less than the critical value. Hopf-bifurcation occurs when the value of delay parameter is greater than the critical value. In additional, we calculate the sensitivity analysis of the dynamics system to understand, how the various source of uncertainty in a model contributes the overall uncertainty.