Mathematical Modeling And Analysis Of Stability In Dynamical System Critically Affected By Increasing Rate Of Infertility In Species: Reproductive Toxicology

Abstract

In this paper, the solution of a nonlinear differential model is obtained to find out the critical solution for a reprotoxic dynamical system. The dynamical system is about a habitat in which some of the species are living under the harmful effect of reprotoxin emitting from the external sources. Here, we considered the simultaneous effects of reprotoxins, one of which is considered as the more reprotoxic than the other or becoming more reprotoxic in the presence of the other. Uptake of reprotoxins by the biological species altered the various functions of the organs. Also it produces its effects on the organs related to the reproductive system which is not only complex but the process of reproduction performed in multiple steps. These reprotoxicity consequences can occur in various forms including additive, combined, or synergistic form, and found that the harmful effect exhibited is more effective than the single one. Here, we obtain the stability analysis at the equilibrium point in which the numerical stability for the proposed model characterizes the stability of a dynamical system in the region of attraction. The mathematical structures stability withstand the decreasing of the steady state of the dynamical system for the changing value of uncontrolled parameters especially the increase rate of the reprotoxin in the environment. This will help in analyzing the energy dissipation capacity of the dynamical model undergoing the effect of controlled and uncontrolled parameters, thus allowing stopping the damage in the structural parameters responsible for divergent of the trajectory path away from the equilibrium point. Another approach that is being utilized in the dynamical system is to provide the external visualization of variation of varying parameters in multidirectional path i.e. changing one and keeping the other parameters constant, estimating the point where the diminishing or the collapse of the system can occur. The main purpose of this paper is to examine the stability both local as well as global of the dynamical system via using mathematical tools and mathematical structural stability to understand the movement of trajectory path towards the fixed point in the attractor basin of the dynamical system.