MATHEMATICAL MODELLING OF PREY AND PREDATOR SPECIES WITH TWO AGE GROUPS OF PREY POPULATION
By
V. P. Saxena¹ and Lalita Dhurve²
¹Jiwaji University, Gwalior-, Madhya Pradesh, India-474011
²Department of Mathematics, Government. Science College Pandhurn, Madhya Pradesh , India-480334,
Email: vinodpsaxena@gmail.com, lalitasingh245@gmail.com
(Received: August 17, 2023; In format : October 09, 2023; Revised: December 28, 2023; Accepted: February 18, 2024)
DOI: https://doi.org/10.58250/jnanabha.2024.54120
Abstract
In this paper we developed mathematical model of prey and predator wild life population of finite size. We consider a prey population can be divided into two age groups. One part of prey species are adults and other part of prey species are juveniles or infants. A mathematical framework has been generated in terms of a system of nonlinear difference equations including all the significant parameters like generation wise per capita birth and death rates, migration of animals of second age group and transition from one age group to another. The solution are worked out in terms of finite multi variable polynomials. If the parameters manipulated by adjusting birth rate etc. in controlled environment in such a way that the polynomials match with standard polynomials in special functions then mathematical analysis can be easily carried out. This can be fruitful in wild life management. Here Numerical computations have been made for the change of populations in successive generations and different values of the parameters. Graphs have been plotted to depict the comparative variations.
2020 Mathematical Sciences Classification: 33C50, 33C90, 33F05.
Keywords and Phrases: Population Dynamics, Wildlife Population, Difference Equations, Classical Polynomials.