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.

Competitiveness of alga Microcystis aeruginosa co-cultivated with cyanobacterium Raphidiopsis raciborskii confirms its dominating position

Microcystis aeruginosa has always been regarded as the main culprit of cyanobacterial blooms in freshwater.However,in recent years,Raphidiopsis raciborskii has gradually replaced M.aeruginosa as the culprit of cyanobacterial blooms in some tropical and subtropical shallow lakes.To reveal which one plays a more dominant role,interactions between cylindrospermospin(CYN)-producing R.raciborskii and microcystins(MCs)-producing or non-MCs-producing M.aeruginosa strains were studied using bialgal cultures at different initial ratios of biomasses of the two species at 25℃.During the co-cultivation,the M.aeruginosa strains inhibited the growth and heterocyst formation of R.raciborskii filaments,and thus occupied a dominant position during the co-cultivation regardless of the initial biomass ratios in the cultures.In addition,the MCs-producing M aeruginosa strain contributed to a higher portion of the total biomass and exerted a stronger inhibitory effect on R.raciborskii compared with the non-MCs-producing strain.However,the growth of both MCs-producing and non-MCs-producing M.aeruginosa strains was stimulated by R.raciborskii in the co-cultures compared with M.aeruginosa monoculture,indicating that M.aeruginosa could outcompete R.raciborskii if given enough time,enabling it to develop into the dominant species even in very low initial concentration.To our best knowledge,this is the first report on the loss of heterocyst formation by a species of cyanobacteria that resulted from interactions between two different species of cyanobacteria.These findings indicate that it is difficult for R.raciborskii to replace the dominant position of M.aeruginosa under the experimental environmental condition,and the allelopathic effects of M.aeruginosa on R.raciborskii could significantly contribute to the success of M.aeruginosa.

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.

HOMOCLINIC BIFURCATION IN SEMI-CONTINUOUS DYNAMIC SYSTEMS

In this paper, a class of homoclinic bifurcations in semi-continuous dynamic systems are investigated. On the basis of rotated vector fields theory, existence of order-1 periodic solution and the rotated vector fields of the semi-continuous dynamic system are discussed. Furthermore, homoclinic cycles and homoclinic bifurcations are described. Finally, an example is provided to show the validity of our theoretical results.