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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. [ABSTRACT FROM AUTHOR]

By taking into account various food components in the ecosystem, the research intends to develop a set of difference equations to simulate a plant-herbivore interaction of Holling Type II. We determine the local stability of the equilibrium points for the scenarios of extinction, semi-extinction (extinction for one species), and coexistence using the Linearized Stability Theorem. For a suitable Lyapunov function, we investigate theoretical findings to determine the global stability of the coexisting equilibrium point. It is clear that the system exhibits both Flip and Neimark-Sacker bifurcation under particular circumstances using the central manifold theorem and the bifurcation theory. Numerical simulations are done by MATLAB which are used to validate our conclusions. [ABSTRACT FROM AUTHOR]

In this paper an SIS epidemic model with saturated incidence rate and treatment function is proposed and studied. The existence of all feasible equilibrium points is discussed. The local stability conditions of the disease free equilibrium point and endemic equilibrium point are established with the help of basic reproduction number. However the global stability conditions of these equilibrium points are established using Lyapunov method. The local bifurcation near the disease free equilibrium point is investigated. Hopf bifurcation condition, which may occurs around the endemic equilibrium point is obtained. The conditions of backward bifurcation and forward bifurcation near the disease free equilibrium point are also determined. Finally, numerical simulations are given to investigate the global dynamics of the system and confirm the obtained analytical results. [ABSTRACT FROM AUTHOR]