Mutualistic behaviour in an interaction model of small fish, remora and large fish

Abstract

For this study, a three-species food chain model that considers interactions between small fish, remora fish, and large fish has been developed. It is assumed that large fish consume small fish through the functional response of Holling type II. Remora fish are considered to benefit from eating the remaining parts of small fish hunted by larger fish. Remora fish may benefit from eating the parasites found in the bodies of large fish. The non-negativity and boundedness of the solution of the model are investigated. In addition, each potential stable state for the model has been determined. We also investigated the local stability of the model, which is close to the steady state. The Lyapunov function and geometric technique are used to investigate the global stability of the model. It has been found that the increase in the refuge rate for small fish contributes to the instability of the model. It has been observed that the model may show unstable behaviour due to an increase in the rate of consumption of small fish by big fish. It has been found that the density of remora fish may rise because of their mutualistic relationship with large fishes.