Abstract
In this paper, a fractional-order Hastings-Powell food chain model is discussed. It is assumed that the top-predator population is supported by alternative food. Existence and local stability of equilibrium points of fractional-order system are investigated. Numerical simulations are conducted to illustrate analysis results. The analysis results show that alternative food can give a positive impact for top-predator population. Keywords: Alternative food, Fractional-order, Grunwald-Letnikov approximation, Hasting-Powell model, Stability.
Highlights
Nowadays, fractional calculus becomes the main focus for the researchers
Many interesting fenomena in ecology can be described by mathematical model through predator-prey models such as harvesting in predator population [1], supplying alternative food in a predator population [2], refuging prey population [3], spreading disease in ecosystem [4], and the effect of the present an omnivore [5]
In predator prey model [2], it is assumed that prey populations do not always exist, they experience migration to find new habitats due to climate change factors and low food reserves
Summary
Fractional calculus becomes the main focus for the researchers. Many problems of science and engineering can be modeled by using fractional derivatives. Interactions between populations can be described in a food chain model. One of the interactions in the food chain is predation process. Many interesting fenomena in ecology can be described by mathematical model through predator-prey models such as harvesting in predator population [1], supplying alternative food in a predator population [2], refuging prey population [3], spreading disease in ecosystem [4], and the effect of the present an omnivore [5]. In predator prey model [2], it is assumed that prey populations do not always exist, they experience migration to find new habitats due to climate change factors and low food reserves. A food chain model of threespecies fractional-order with alternative food is introduced. Numerical simulations are illustrated by the GrunwaldLetnikov approximation [8]
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