Analysis of a Fractional Stage-Structured Model With CrowleyMartin Type Functional Response by Lagrange Polynomial Based Method
- Title
- Analysis of a Fractional Stage-Structured Model With CrowleyMartin Type Functional Response by Lagrange Polynomial Based Method
- Creator
- Baishya C.; Veeresha P.
- Description
- The dynamics of a stage-structured predator-prey system that replicates interactions between two densities of prey and predator populations were investigated in this work. The adult predator population and the juvenile predator are the two compartments that make up the predator population in the model. The predator relies on both prey and juvenile predator, which is another element of the paradigm that can be termed cannibalism. CrowleyMartin type functional denotes the nature of the interaction between prey and adult predators, while Holling type-I functional response denotes the nature of contact between juvenile and adult predators. The concept of memory is introduced in the form of the Caputo fractional derivative to reflect the complicated dynamics of interaction among the species. As a result, the model is able to incorporate all relevant historical information about the occurrence, from its inception to the desired time, into its calculations. We have also investigated the boundedness and existence and uniqueness of solutions to the proposed model. The condition of existence and stability of various points of equilibrium are investigated. The numerical simulations are performed by using the Lagrange polynomial-based method which is novel in the field of mathematical biology. Simulations have been accomplished to examine the significance of parameters related to cannibalism, the conversion rate from prey to adult predator, harvesting of an adult predator, and growth rate of juvenile predators on the overall behavior of the system. The noteworthy performance of the fractional operator on the anticipated predator-prey models dynamical behavior is well demonstrated by numerical results. The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023.
- Source
- Studies in Computational Intelligence, Vol-1109, pp. 149-180.
- Date
- 2023-01-01
- Publisher
- Springer Science and Business Media Deutschland GmbH
- Subject
- Caputo fractional derivative; CrowleyMartin type functional response; Holling type; Lagrange polynomial based method; Stage-structured model
- Coverage
- Baishya C., Department of Studies and Research in Mathematics, Tumkur University, Tumkur, 572103, India; Veeresha P., Department of Mathematics, Center for Mathematical Needs, CHRIST (Deemed to be University), Bengaluru, 560029, India
- Rights
- Restricted Access
- Relation
- ISSN: 1860949X
- Format
- Online
- Language
- English
- Type
- Book chapter
Collection
Citation
Baishya C.; Veeresha P., “Analysis of a Fractional Stage-Structured Model With CrowleyMartin Type Functional Response by Lagrange Polynomial Based Method,” CHRIST (Deemed To Be University) Institutional Repository, accessed February 23, 2025, https://archives.christuniversity.in/items/show/18396.