The role of amensalism and parasitism on the dynamics of three species ecological system

This paper introduces a novel mathematical model of a three-species ecosystem that includes biological relationships such as amensalism and parasitism. Unlike most previous studies, it assumed that the ecosystem consists of three different kinds of interactions at the same time: two host–parasite interactions, while the third one is amensal–enemy interactions. To do the dynamic analysis of this system, all of the solution’s attributes were examined, and potential equilibrium points were found. The local stability was established using the linearization technique. The global stability was examined using Lyapunov functions. Every prerequisite for perseverance was identified. The effects of varying the parameters were investigated using the bifurcation theory. A computer simulation was applied to bolster our analytical research. It is observed that the proposed model has a globally stable coexistence point, while the periodic dynamics do not exist. The impact of amensalism and parasitism is clearly shown due to the transition of the solution from the coexistence point to the planar equilibrium points once their rates exceed a vital value, and conversely, it is proved that the system (3) undergoes a transcritical bifurcation near the first axial and the enemy–host-free equilibrium points.