STUDY THE DYNAMICAL ANALYSIS OF DEFORM BIOLOGICAL POPULATION DUE TO PROLONGATION IN EXTERNALLY BY EMITTED TOXICANTS
By
Digvijai Singh1, Joydip Dhar2 , Alok Kumar Agrawal3 and Suyash Narayan Mishra4
1,3Department of Mathematics, Amity School of Applied Sciences, Lucknow, Uttar Pradesh, India-226028
2Department of Engineering Sciences, ABV-Indian Institute of Information Technology and Management, Gwalior, Madhya Pradesh, India-474015
4Applied Sciences and Humanities Department, Institute of Engineering and Technology, Lucknow, Uttar Pradesh, India-226021
Email: dig.singh1@s.amity.edu, jdhar@iiitm.ac.in, akagrawal@lko.amity.edu and snmishra@ietlucknow.ac.in
(Received: September 26, 2024; In format: February 22, 2025; Revised: March 04, 2025, Accepted: March 10, 2025)
DOI: https://doi.org/10.58250/jnanabha.2025.55106
Abstract
Each biological species has its structure, which provides its existence in the atmosphere. But in the last few decades, there has been an abnormal change in their structure due to the externally emitted toxicant. These changes have a terrible impact on the atmosphere. In this prescribed model, we are proposing and analyzing the effect of externally emitted toxicants on a population model accompanied by the deformation delay and the delay in the depletion of toxicants. The dynamical nature and local stability of the model have been checked, and results show that during the absence of the deformation delay, the system is locally stable for toxicant delay at coexisting equilibrium points. But when both delays exist during the procedure, the biological population system becomes unstable,i.e., as the deformation delay increases, the system’s stability is distributed and reaches a critical value of deformation delay, and the system exhibits Hopf bifurcation. Finally, the numerical authentication of experimental results has been validated by the numerical simulation of the designed model
2020 Mathematical Sciences Classification: 92K25, 37N25, 34D20, 34K18, 37M05.
Keywords and Phrases: Deform Population Dynamics, Dynamical Analysis, Stability Theory, Hopf Bifurcation and Numerical Simulation