Stability (learning theory)

Physics

Operator (biology)

Presumption

Mathematics

Dynamical systems theory

Transcription factor

Biology

Gene

Machine learning

Fractional calculus

Mathematical analysis

Political science

Predation

Repressor

Chemistry

Ecology

Geometry

Computer science

Quantum mechanics

Differential equation

Applied mathematics

Product (mathematics)

Ordinary differential equation

Biochemistry

Advances in Difference Equations

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.

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