A mathematical model for chemical defense mechanism of two competing species

In this paper, a non-linear mathematical model is proposed and analyzed to study the phenomenon of a chemical defense mechanism involving two competing species, where each species produces a toxicant affecting the other. It is shown that if the emission rate coefficient of toxicant, produced by one species increases, the equilibrium density of the other species decreases and its magnitude is lower than its original carrying capacity. It is found that the usual principle of competitive exclusion (coexistence) in the absence of toxicant may change in the case under consideration. It is also observed that increases in the values of production rates of toxicants by the competing species and depletion rates of environmental toxicants due to its assimilation by the species has a destabilizing effect, and decrease in the washout rates of environmental toxicants has a destabilizing effect on the dynamics of the system. In the case of allelopathy, where only one species produces a toxicant affecting the other species, it is shown that the affected species is driven to extinction for large production rate of this toxicant.