Dynamical analysis of an aquatic amensalism model with non-selective harvesting and Allee effect

Dynamical behaviours of discrete amensalism system with fear effects on first species

Amensalism, a rare yet impactful symbiotic relationship in ecological systems, is the focus of this study. We examine a discrete-time amensalism system by incorporating the fear effect on the first species. We identify the plausible equilibrium points and analyze their local stability conditions. The global attractivity of the positive equilibrium, $ E^* $, and the boundary equilibrium, $ E_1 $, are analyzed by exploring threshold conditions linked to the level of fear. Additionally, we analyze transcritical bifurcations and flip bifurcations exhibited by the boundary equilibrium points analytically. Considering some biologically feasible parameter values, we conduct extensive numerical simulations. From numerical simulations, it is observed that the level of fear has a stabilizing effect on the system dynamics when it increases. It eventually accelerates the extinction process for the first species as the level of fear continues to increase. These findings highlight the complex interplay between external factors and intrinsic system dynamics, enriching potential mechanisms for driving species changes and extinction events.

Dynamic analysis of a new aquatic ecological model based on physical and ecological integrated control

Within the framework of physical and ecological integrated control of cyanobacteria bloom, because the outbreak of cyanobacteria bloom can form cyanobacteria clustering phenomenon, so a new aquatic ecological model with clustering behavior is proposed to describe the dynamic relationship between cyanobacteria and potential grazers. The biggest advantage of the model is that it depicts physical spraying treatment technology into the existence pattern of cyanobacteria, then integrates the physical and ecological integrated control with the aggregation of cyanobacteria. Mathematical theory works mainly investigate some key threshold conditions to induce Transcritical bifurcation and Hopf bifurcation of the model (2.1), which can force cyanobacteria and potential grazers to form steady-state coexistence mode and periodic oscillation coexistence mode respectively. Numerical simulation works not only explore the influence of clustering on the dynamic relationship between cyanobacteria and potential grazers, but also dynamically show the evolution process of Transcritical bifurcation and Hopf bifurcation, which can be clearly seen that the density of cyanobacteria decreases gradually with the evolution of bifurcation dynamics. Furthermore, it should be worth explaining that the most important role of physical spraying treatment technology can break up clumps of cyanobacteria in the process of controlling cyanobacteria bloom, but cannot change the dynamic essential characteristics of cyanobacteria and potential grazers represented by the model (2.1), this result implies that the physical spraying treatment technology cannot fundamentally eliminate cyanobacteria bloom. In a word, it is hoped that the results of this paper can provide some theoretical support for the physical and ecological integrated control of cyanobacteria bloom.

Complex Dynamics Analysis of a Discrete Amensalism System with a Cover for the First Species

Of interest is the dynamics of the discrete-time amensalism model with a cover on the first species. We first obtain the existence and stability of fixed points and the conditions for the permanent coexistence of two species. Then we demonstrate the occurrence of flip bifurcation by using the central manifold theorem and bifurcation theory. A hybrid control strategy is used to control the flip bifurcation and stabilize unstable periodic orbits embedded in the complex attractor. Numerical simulation verifies the feasibility of theoretical analysis and reveals some novel and exciting dynamic phenomena.