On the stability and Hopf-bifurcation of a multi-delayed competitive population system affected by toxic substances with imprecise biological parameters

In this paper we have analyzed the stability and Hopf-bifurcation behaviors of a multi-delayed two-species competitive system affected by toxic substances with imprecise biological parameters. We have exercised a method to handle these imprecise biological parameters by using parametric form of interval numbers. We have studied the feasibility of various equilibrium points and their stability. In case of toxic stimulatory system, the delay model exhibits a stable limit cycle oscillation due to variation in the delay parameters which lead to Hopf-bifurcation. Numerical simulations with a hypothetical set of data have been done to support the analytical findings.