Global stability analysis of a general Leslie type prey-predator system involving harvesting and refuge effect
Abstract
We consider a general Leslie type prey-predator system involving harvesting and refuge effects. In the model, we use a general function to define how the population of prey grows. In this paper, we explore dynamical behavior of this system by taking three different growth forms for prey, namely, (a) exponential growth, (b) logistic growth and (c) logistic growth including Allee effect, respectively. For each model, we present global stability analysis by applying linear stability theory, utilizing Bendixson-Dulac criteria and constructing an appropriate Lyapunov function, respectively. From a mathematical point of view, we have concluded that harvesting and refuge have no effects on global stability of each model's consistent condition. Furthermore, we investigate the impacts of an external harvesting and a refuge for prey population on densities of prey and predator species. Mathematical analysis yields the result that prey population density decreases under the harvesting effect and increases under the refuge effect, while predator population density decreases as the harvesting and refuge effects increase. At last, in order to support analytical results and also to explore further impacts of prey refuge and harvesting on dynamics, we perform numerical simulations. We numerically discuss their impacts on the densities in early time. The results obtained underline that these effects are important for the continuation of the balanced functioning between prey and predator species, so they should be accounted into prey-predator models together.
Keywords
References
- 1] W.C. Allee, Animal Aggregations, A Study in General Sociology, Chicago, USA: University of Chicago Press, 1931.
Details
Primary Language
English
Subjects
Ordinary Differential Equations, Difference Equations and Dynamical Systems, Biological Mathematics, Dynamical Systems in Applications
Journal Section
Research Article
Early Pub Date
May 18, 2026
Publication Date
-
Submission Date
August 1, 2024
Acceptance Date
March 30, 2026
Published in Issue
Year 2026 Number: Advanced Online Publication
APA
Baydemir, P., & Merdan, H. (2026). Global stability analysis of a general Leslie type prey-predator system involving harvesting and refuge effect. Hacettepe Journal of Mathematics and Statistics, Advanced Online Publication. https://doi.org/10.15672/hujms.1525671
AMA
1.Baydemir P, Merdan H. Global stability analysis of a general Leslie type prey-predator system involving harvesting and refuge effect. Hacettepe Journal of Mathematics and Statistics. 2026;(Advanced Online Publication). doi:10.15672/hujms.1525671
Chicago
Baydemir, Pinar, and Hüseyin Merdan. 2026. “Global Stability Analysis of a General Leslie Type Prey-Predator System Involving Harvesting and Refuge Effect”. Hacettepe Journal of Mathematics and Statistics, no. Advanced Online Publication. https://doi.org/10.15672/hujms.1525671.
EndNote
Baydemir P, Merdan H (May 1, 2026) Global stability analysis of a general Leslie type prey-predator system involving harvesting and refuge effect. Hacettepe Journal of Mathematics and Statistics Advanced Online Publication
IEEE
[1]P. Baydemir and H. Merdan, “Global stability analysis of a general Leslie type prey-predator system involving harvesting and refuge effect”, Hacettepe Journal of Mathematics and Statistics, no. Advanced Online Publication, May 2026, doi: 10.15672/hujms.1525671.
ISNAD
Baydemir, Pinar - Merdan, Hüseyin. “Global Stability Analysis of a General Leslie Type Prey-Predator System Involving Harvesting and Refuge Effect”. Hacettepe Journal of Mathematics and Statistics. Advanced Online Publication (May 1, 2026). https://doi.org/10.15672/hujms.1525671.
JAMA
1.Baydemir P, Merdan H. Global stability analysis of a general Leslie type prey-predator system involving harvesting and refuge effect. Hacettepe Journal of Mathematics and Statistics. 2026. doi:10.15672/hujms.1525671.
MLA
Baydemir, Pinar, and Hüseyin Merdan. “Global Stability Analysis of a General Leslie Type Prey-Predator System Involving Harvesting and Refuge Effect”. Hacettepe Journal of Mathematics and Statistics, no. Advanced Online Publication, May 2026, doi:10.15672/hujms.1525671.
Vancouver
1.Pinar Baydemir, Hüseyin Merdan. Global stability analysis of a general Leslie type prey-predator system involving harvesting and refuge effect. Hacettepe Journal of Mathematics and Statistics. 2026 May 1;(Advanced Online Publication). doi:10.15672/hujms.1525671