A bifurcation study: effect of a toxicant on a biological species, emitted by itself in its own environment

  • A.K. Agrawal Amity University, Lucknow
  • Anuj Kumar Integral University, Lucknow
Keywords: Biological population, mathematical model, toxicant, supercritical hopfbifurcation

Abstract

In this paper, a model based on effect of toxicant on a biological species [1, chap. 2] is analyzed for the existence and nature of hopf-bifurcation. The biological population is logistically growing in its own environment and toxicant is being emitted by the population itself. The hopf-bifurcation analysis of model shows that when the emission rate of toxicant by the biological population increases in the environment, the density level of biological population decreases and after crossing a critical value of emission rate, the density of biological population starts oscillating and never settle down to its equilibrium level. The hopf-bifurcation analysis of model increases the validity of model. The dynamic behavior of the model for the emission rate of toxicant is described by providing numerical simulation

Author Biographies

A.K. Agrawal, Amity University, Lucknow

Department of Mathematics

Amity University

Anuj Kumar, Integral University, Lucknow

Department of Mathematics

Integral University

Published
2016-03-31
How to Cite
[1]
A. Agrawal and A. Kumar, “A bifurcation study: effect of a toxicant on a biological species, emitted by itself in its own environment”, EPH - International Journal of Science And Engineering (ISSN: 2454 - 2016), vol. 2, no. 3, pp. 13-24, Mar. 2016.