Search

This paper investigates a two-species amensalism model that includes the fear effect on the first species and the Beddington–DeAngelis functional response. The existence and stability of possible equilibria are investigated. Under different parameters, there exist two stable equilibria which means that this model is not always globally asymptotically stable. Together with the existence of all possible equilibria and their stability, saddle connection and close orbits, we derive some conditions for transcritical bifurcation and saddle-node bifurcation. Furthermore, global dynamics analysis of the model is performed. It is observed that under certain parameter conditions, when the intensity of the fear effect is below a certain threshold value, as the fear effect increases it will only reduce the density of the first species population and will have no influence the extinction or existence of the first species population. However, when the fear effect exceeds this threshold, the increase of the fear effect will accelerate the extinction of the first species population. Finally, numerical simulations are performed to validate theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with a reaction–diffusion–advection chemostat model with two species growing and competing for a single-limited resource. By taking the growth rates of the two species as variable parameters, we study the effect of growth rates on the dynamics of this system. It is found that there exist several critical curves, which may classify the dynamics of this system into three scenarios: (1) extinction of both species; (2) competitive exclusion; (3) coexistence. Moreover, we take numerical approaches to further understand the potential behaviors of the above critical curves and observe that the bistable phenomenon can occur, besides competitive exclusion and coexistence. To further study the effect of advection and diffusion on the dynamics of this system, we present the bifurcation diagrams of positive equilibrium solutions of the single species model and the two-species model with the advection rates and the diffusion rates increasing, respectively. These numerical results indicate that advection and diffusion play a key role in determining the dynamics of two species competing in a flow reactor. [ABSTRACT FROM AUTHOR]