In the paper, under the framework of exploring the interaction between algae and bacteria, an algae-bacteria ecological model was established to analyze the interaction mechanism and growth coexistence mode between al...In the paper, under the framework of exploring the interaction between algae and bacteria, an algae-bacteria ecological model was established to analyze the interaction mechanism and growth coexistence mode between algicidal bacteria and algae. Firstly, mathematical work mainly provided some threshold conditions to ensure the occurrence of transcritical bifurcation and saddle-node bifurcation, which could provide certain theoretical support for selecting key ecological environmental factors and numerical simulations. Secondly, the numerical simulation work dynamically displayed the evolution process of the bifurcation dynamic behavior of the model (2.1) and the growth coexistence mode of algae and algicidal bacteria. Finally, it was worth summarizing that intrinsic growth rate and combined capture effort of algae population had a strong influence on the dynamic behavior of the model (2.1). Furthermore, it must also be noted that transcritical bifurcation and saddle-node bifurcation were the inherent driving forces behind the formation of steady-state growth coexistence mode between algicidal bacteria and algae. In summary, it was hoped that the results of this study would contribute to accelerating the study of the interaction mechanism between algicidal bacteria and algae.展开更多
Under the control framework of algae bloom in eutrophic lakes and reservoirs based on biological manipulation, the temperature variable is introduced into ecological modeling to show that it is a necessary condition f...Under the control framework of algae bloom in eutrophic lakes and reservoirs based on biological manipulation, the temperature variable is introduced into ecological modeling to show that it is a necessary condition for the rapid occurrence of algal blooms, and an aquatic ecological model with temperature effect is proposed to describe dynamic relationship between algae and biological manipulation predator. The mathematical theory work mainly investigates the existence and stability of some equilibrium points and some critical conditions for the occurrence of transcritical bifurcation and Hopf bifurcation. The numerical simulation mainly shows the dynamic evolution process of bifurcation dynamics, which can not only verify the validity and feasibility of these theoretical works but also analyze the influence of some key parameters on dynamic behavior evolution. Furthermore, It is worth emphasizing that temperature plays an important role in the coexistence of algae and biological manipulation predators. Moreover, the coexistence mode of algae and biological manipulation predators is discovered by means of dynamic bifurcation evolution. Finally, it is hoped that these research results can provide some reference for the study of aquatic ecosystems.展开更多
文摘In the paper, under the framework of exploring the interaction between algae and bacteria, an algae-bacteria ecological model was established to analyze the interaction mechanism and growth coexistence mode between algicidal bacteria and algae. Firstly, mathematical work mainly provided some threshold conditions to ensure the occurrence of transcritical bifurcation and saddle-node bifurcation, which could provide certain theoretical support for selecting key ecological environmental factors and numerical simulations. Secondly, the numerical simulation work dynamically displayed the evolution process of the bifurcation dynamic behavior of the model (2.1) and the growth coexistence mode of algae and algicidal bacteria. Finally, it was worth summarizing that intrinsic growth rate and combined capture effort of algae population had a strong influence on the dynamic behavior of the model (2.1). Furthermore, it must also be noted that transcritical bifurcation and saddle-node bifurcation were the inherent driving forces behind the formation of steady-state growth coexistence mode between algicidal bacteria and algae. In summary, it was hoped that the results of this study would contribute to accelerating the study of the interaction mechanism between algicidal bacteria and algae.
文摘Under the control framework of algae bloom in eutrophic lakes and reservoirs based on biological manipulation, the temperature variable is introduced into ecological modeling to show that it is a necessary condition for the rapid occurrence of algal blooms, and an aquatic ecological model with temperature effect is proposed to describe dynamic relationship between algae and biological manipulation predator. The mathematical theory work mainly investigates the existence and stability of some equilibrium points and some critical conditions for the occurrence of transcritical bifurcation and Hopf bifurcation. The numerical simulation mainly shows the dynamic evolution process of bifurcation dynamics, which can not only verify the validity and feasibility of these theoretical works but also analyze the influence of some key parameters on dynamic behavior evolution. Furthermore, It is worth emphasizing that temperature plays an important role in the coexistence of algae and biological manipulation predators. Moreover, the coexistence mode of algae and biological manipulation predators is discovered by means of dynamic bifurcation evolution. Finally, it is hoped that these research results can provide some reference for the study of aquatic ecosystems.
