EXISTENCE OF HOPF-BIFURCATION IN A MATHEMATICAL MODEL ON DEPLETION OF GRASSLAND UNDER THE CATASTROPHIC EFFECT OF INVASIVE SPECIES IN KAZIRANGA NATIONAL PARK (KNP), ASSAM, INDIA
The grasslands of Kaziranga National Park, Assam, India, have been threatened by certain species of plants such as Mikenia, Mimosa, Simul (Bombax ceiba) etc. These plants are found to be invasive and without efforts to control their growth the grasslands along with their wildlife could face catastrophic situation. Controlled annual burning, manual weed removal, stubbing are some of the control measures the park has been employing in this regard. Taking the cumulative densities of all the invasive species of plants which affect the grasslands as bad biomass and employing effort to control their growth for healthy grassland density, this paper attempts to study the long term effect of bad biomass on grassland biomass using non-linear mathematical model. For this, the feasible equilibria of the model was obtained and their local stability discussed. Through qualitative analysis it was observed that grassland density could be maintained at equilibrium with proper effort. It was also observed that reducing the effort could adversely affect the dynamics of the system. When the effort was reduced beyond a certain value, Hopf bifurcation was observed. These findings were validated through numerical simulation.
Keywords: Grassland biomass, Depreciation, Stability, Hopf-bifurcation.