Environment and Ecology Research Vol. 10(5), pp. 519 - 541
DOI: 10.13189/eer.2022.100501
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Nonlinear Modeling and Stability Analysis of Simultaneous Effects of Reprotoxins in Dynamic Systems of Biological Species at Fixed Points and Their Control

Chetna Singh ^1,*, Alok Agrawal ¹, Amresh Kumar ², Anuj Kumar Agarwal ³, Piyush Kumar Tripathi ^1
1 Department of Mathematics, Amity University, Lucknow, Uttar Pradesh, India
² Department of Mathematics, Babu Banarasi Das Northern Institute of Technology Lucknow, India
³ Department of Mathematics, Babu Banarasi Das University, Lucknow, India

ABSTRACT

Using a non-linear differential model, investigations were conducted to determine the harmful effects of two reprotoxins simultaneously in the reproduction process of the biological species. Reprotoxins are chemicals that have been shown to cause cancer in various parts of the reproductive system due to their effect on biological species and getting affected as their multistep protection network fails. The simultaneous effect shows various harmful effects depending upon the increasing concentration level or the quantity of uptake doses. Reprotoxin enters the body in various ways and produces deformities in various parts of the reproductive system. It can be seen in various forms including additive form, multiplicative form, or synergistic form. Both direct and indirect reprotoxin have a harmful impact on the reproduction process. Here, in this paper, we provide stability analysis at the equilibrium points for numerical solutions that characterise solutions of dynamical behaviour based on the parameters that are being used in the formulation of the systems. Toxification and detoxification, as well as some repair, occur inside the cell, organ, or other sites of the reproduction system. This includes enhanced protein synthesis to replace damaged or non-functioning proteins. The goal of this work is to determine the circumstances or the level of growing reprotoxin at which the system is said to become entirely destabilized. To comprehend the movement of the trajectory path in the attractor basin towards or away from the fixed point, different mathematical structures have been developed. It concludes that the level of a species' population may be preserved by regulating the amount of various reprotoxins in the environment.

KEYWORDS
Mathematical Model, Reproductive Toxicant, Reproduction, Biological Species, Mathematical Structure

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Chetna Singh , Alok Agrawal , Amresh Kumar , Anuj Kumar Agarwal , Piyush Kumar Tripathi , "Nonlinear Modeling and Stability Analysis of Simultaneous Effects of Reprotoxins in Dynamic Systems of Biological Species at Fixed Points and Their Control," Environment and Ecology Research, Vol. 10, No. 5, pp. 519 - 541, 2022. DOI: 10.13189/eer.2022.100501.

(b). APA Format:
Chetna Singh , Alok Agrawal , Amresh Kumar , Anuj Kumar Agarwal , Piyush Kumar Tripathi (2022). Nonlinear Modeling and Stability Analysis of Simultaneous Effects of Reprotoxins in Dynamic Systems of Biological Species at Fixed Points and Their Control. Environment and Ecology Research, 10(5), 519 - 541. DOI: 10.13189/eer.2022.100501.