CAPUTO DERIVATIVE FRACTIONAL ORDER PREY-PREDATOR MODEL AND MATHEMATICAL ANALYSIS
Abstract
A foundational process in the field of ecology is the interaction between prey and predator. This interaction refers to the changes in the population density of two species in relation to each other, due to the fact that prey and predator share the same environment and one species preys on the other. The application of differential equations, otherwise referred to as Lotka-Volterra equations, in modeling prey-predator systems is of significant importance in studying the dynamics of interacting biological populations. Prey-predator models are population models that show the relationship between two species sharing the same environment. The present study involves the analysis of stability and the numerical solutions of a discrete-time fractional-order predator-prey mathematical model. This model is divided into two compartments: the prey population (N) and the predator population (P). The Caputo sense is employed to utilize the notion of a fractional derivative. The numerical results obtained for the prey-predator fractional mathematical model were achieved through the implementation of the Euler method, thus yielding graphs for visualization. The results show that the prey population increases steadily over time, while the predator population also increases gradually and steadily.
Keywords
Fractional-Order Prey-Predator Population Model, Mathematical Modeling, Euler Method, Caputo Derivative, Stability Analysis
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