Dynamical behavior of two predators–one prey model with generalized functional response and time-fractional derivative

Advances in Difference Equations

article

Djilali, Salih¹  Ghanbari, Behzad³ 

[1] Laboratoire d’Analyse Non Linéaire et Mathématiques Appliquées, Université de Tlemcen;Department of Mathematics, Faculty of Exact Sciences and Informatics, Hassiba Benbouali University;Department of Engineering Science, Kermanshah University of Technology;Department of Mathematics, Faculty of Engineering and Natural Sciences, Bahçeşehir University

关键词: Predator–prey model;    Generalized functional response;    Predator competition;    Fractional calculus;    Sensitivity analysis;   

DOI  :  10.1186/s13662-021-03395-9

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

The behavior of any complex dynamic system is a natural result of the interaction between the components of that system. Important examples of these systems are biological models that describe the characteristics of complex interactions between certain organisms in a biological environment. The study of these systems requires the use of precise and advanced computational methods in mathematics. In this paper, we discuss a prey–predator interaction model that includes two competitive predators and one prey with a generalized interaction functional. The primary presumption in the model construction is the competition between two predators on the only prey, which gives a strong implication of the real-world situation. We successfully establish the existence and stability of the equilibria. Further, we investigate the impact of the memory measured by fractional time derivative on the temporal behavior. We test the obtained mathematical results numerically by a proper numerical scheme built using the Caputo fractional-derivative operator and the trapezoidal product-integration rule.

【 授权许可】

CC BY