EXISTENCE OF SUBCRITICAL HOPF BIFURCATION WHEN TWO TOXICANTS ARE AFFECTING A BIOLOGICAL SPECIES

Existence of subcritical Hopf-bifurcation in a mathematical model based on simultaneous effect of two toxicants on a biological species [1; ch.3] is considered, in this paper. Here, the biological species is growing logistically in its habitat which is simultaneously affected by two different toxicants, the first toxicant is being emitted by some external sources and the second toxicant is discharged by the biological species itself through its various actions (such as household discharge, vehicular exhaust, industrial effluents, in the case of human population). We have shown that the model undergoes a subcritical Hopf-bifurcation at the critical value of emission rate of toxicant by biological species itself ????. The analysis of Hopf-bifurcation shows that the density of biological species ???? is stable but after crossing the critical level of ????, density of biological species becomes zero.