Dynamic Analysis of an Algae-Bacteria Ecological Model

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.

Dynamic Analysis of an Algae-Fish Harvested Model with Allee Effect

In this paper, an algae-fish harvested model with Allee effect was established to further explore the dynamic evolution mechanism under the influence of key factors. Mathematical theoretical work not only investigated the existence and stability of all possible equilibrium points, but also probed into the occurrence of transcritical and Hopf bifurcation. The numerical simulation works verified the effectiveness of the theoretical derivation results and displayed rich bifurcation dynamical behaviors, which showed that Allee effect and harvest have played a vital role in the dynamic relationship between algae and fish. In summary, it was expected that these research results would be beneficial for promoting the study of bifurcation dynamics in aquatic ecosystems.

The Dynamical Behavior of a Predator-Prey System with Holling Type II Functional Response and Allee Effect

In this paper, we mainly considered the dynamical behavior of a predator-prey system with Holling type II functional response and Allee-like effect on predator, including stability analysis of equilibria and Hopf bifurcation. Firstly, we gave some sufficient conditions to guarantee the existence, the local and global stability of equilibria as well as non-existence of limit cycles. By using the cobweb model, some cases about the existence of interior equilibrium are also illustrated with numerical outcomes. These existence and stability conclusions of interior equilibrium are also suitable in corresponding homogeneous reaction-diffusion system subject to the Neumann boundary conditions. Secondly, we theoretically deduced that our system has saddle-node bifurcation, transcritical bifurcation and Hopf bifurcation under certain conditions. Finally, for the Hopf bifurcation, we choose d as the bifurcation parameter and presented some numerical simulations to verify feasibility and effectiveness of the theoretical derivation corresponding to the existence of yk, respectively. The Hopf bifurcations are supercritical and limit cycles generated by the critical points are stable.

The Dynamical Behavior of a Certain Predator-Prey System with Holling Type II Functional Response

In this paper we analytically and numerically consider the dynamical behavior of a certain predator-prey system with Holling type II functional response, including local and global stability analysis, existence of limit cycles, transcritical and Hopf bifurcations. Mathematical theory derivation mainly focuses on the existence and stability of equilibrium point as well as threshold conditions for transcritical and Hopf bifurcation, which can in turn provide a theoretical support for numerical simulation. Numerical analysis indicates that theoretical derivation results are correct and feasible. In addition, it is successful to show that the dynamical behavior of this predator-prey system mainly depends on some critical parameters and mathematical relationships. All these results are expected to be meaningful in the study of the dynamic complexity of predatory ecosystem.

Global Asymptotic Stability and Hopf Bifurcation in a Homogeneous Diffusive Predator-Prey System with Holling Type II Functional Response

In this paper, we considered a homogeneous reaction-diffusion predator-prey system with Holling type II functional response subject to Neumann boundary conditions. Some new sufficient conditions were analytically established to ensure that this system has globally asymptotically stable equilibria and Hopf bifurcation surrounding interior equilibrium. In the analysis of Hopf bifurcation, based on the phenomenon of Turing instability and well-done conditions, the system undergoes a Hopf bifurcation and an example incorporating with numerical simulations to support the existence of Hopf bifurcation is presented. We also derived a useful algorithm for determining direction of Hopf bifurcation and stability of bifurcating periodic solutions correspond to j ≠0 and j = 0, respectively. Finally, all these theoretical results are expected to be useful in the future study of dynamical complexity of ecological environment.

Harmful algal bloom-forming dinofl agellate Prorocentrum donghaiense inhibits the growth and photosynthesis of seaweed Sargassum fusiformis embryos

Harmful algal bloom(HAB)is an ecological disaster to local mariculture.At present,its impact on macrophytes has not been well studied.In this study,we cultivated sexually propagated embryos of S argassum fusiformis-an edible seaweed-in Prorocentrum donghaiense suspensions at different cell densities(0,0.50×10^(5),0.75×10^(5),1.00×10^(5),and 1.50×10^(5) cells/mL)for 10 days,during which growth and photosynthetic activities of the embryos were determined,and a monocultivation was set up for comparison.Results show that the relative growth rate and photosynthetic activities of the embryos co-cultivated with P.donghaiense were inhibited mostly and significantly in the cell densities of 0.75×10^(5),1.00×10^(5),and 1.50×10^(5) cells/mL,and the inhibitory effects increased in overall with increased cell densities.The maximum relative electron transport rates(rETR max)and apparent photosynthetic efficiency(a)of co-cultivated embryos were all significantly lower than monocultivation ones on the 10 th day.Furthermore,the photosynthetic activity detected by chlorophyll-a fluorescence transient(i.e.,OJIP),the electron transport among electron transfer accepters of PSII(photosystem II)and that from PSII to PSI(photosystem I)was restricted,which is probably responsible for the decreases of rETR max andain the co-cultivated embryos.In addition,parts of the photosynthetic reaction centers of PSII in the co-cultivated embryos were inactivated.Therefore,P.donghaiense bloom could restrain the development and photosynthetic activities of S.fusiformis embryos,reduce the seedlings stock,and eventually hinder the development of S.fusiformis production industry.

Bosonization Approach and Novel Traveling Wave Solutions of the Superfield Gardner Equation

In this paper, the bosonization of the superfield Gardner equation in the case of multifermionic parameters is presented and novel traveling wave solutions are extracted from the coupled bosonic equations by using the mapping and deformation relations. In the case of two-fermionic-parameter bosonization procedure, we provide a special solution in the form of Jacobian elliptic functions. Meanwhile, we discuss and formally derive traveling wave solutions of N fermionic parameters bosonization procedure. This technique can also be applied to treat the N = 1 supersymmetry KdV and mKdV systems which are obtained in two limiting cases.

Population Interaction Dynamics Analysis of an Algae-Fish System

In this paper, before the implementation of ecological laboratory experiments, the population interaction dynamics of an algae-fish system were studied mathematically and numerically. The purpose of this study was to explore how filter-feeding fish population affects the growth dynamics of the algae population. Mathematically theoretical works have been pursuing the investigation of some key conditions for stability of the equilibrium and existence of Hopf bifurcation. Numerical simulation works have been parsing the discovery of the growth dynamics of the algae population in view of population interaction dynamics, which in turn could prove the feasibility of the theoretical derivation and reveal the relationship between filter-feeding fish abundance and algal biomass in fish-drift algae communiyua. Furthermore, it was successful to show that the filter-feeding fish population may be a crucial factor in controlling the proliferation of the algae population, which could also directly grasp the evolution of community dynamics. All these results were expected to be useful in the study of community dynamics and laboratory elimination experiment of the algae population.

Dynamics Analysis of an Aquatic Ecological Model with Allee Effect

In this paper, based on the dynamic relationship between algae and protozoa, an aquatic ecological model with Allee effect was established to investigate how some ecological environment factors affect coexistence mode of algae and protozoa. Mathematical derivation works mainly gave some key conditions to ensure the existence and stability of all possible equilibrium points, and to induce the occurrence of transcritical bifurcation and Hopf bifurcation. The numerical simulation works mainly revealed ecological relationship change characteristics of algae and protozoa with the help of bifurcation dynamics evolution process. Furthermore, it was also worth emphasizing that Allee effect had a strong influence on the dynamic relationship between algae and protozoa. In a word, it was hoped that the research results could provide some theoretical support for algal bloom control, and also be conducive to the rapid development of aquatic ecological models.

Dynamics Analysis of an Aquatic Ecological Model with Temperature Effect

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.