On the Discrete Population Models Without and With the Influence of (k+1)th Previous Generation of Another Species

• Published in: International journal of applied and computational mathematics Vol. 11; no. 2
• Main Authors: Babu, Sibi C., Dilip, D. S.
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.04.2025; Springer Nature B.V
• Subjects: Applications of Mathematics; Bifurcations; Computational Science and Engineering; Mathematical and Computational Physics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Nuclear Energy; Operations Research/Decision Theory; Original Paper; Stability; Theoretical; Persistence; 39A22; Difference equations; Asymptotic behaviour; Boundedness
• ISSN: 2349-5103; 2199-5796
• DOI: 10.1007/s40819-025-01848-3

In this paper, we analyze the stability of two population models of a species, consisting of an equation and a system. The first model represents the growth of a species that depends on its previous and ( k + 1 ) th previous generations without the influence of other species. The second model, a system, represents the growth of a species, which depends on its ( k + 1 ) th previous generation and another species’ previous generation in which the influencing species mutually depend on its ( k + 1 ) th previous generation and the previous generation of the aforesaid species. Moreover, the theorems are verified numerically by animating the plots and bifurcation diagrams to illustrate the boundedness and stability results.