Bifurcation analysis of Leslie-Gower predator-prey system with harvesting and fear effect.

In the paper, a Leslie-Gower predator-prey system with harvesting and fear effect is considered. The existence and stability of all possible equilibrium points are analyzed. The bifurcation dynamic behavior at key equilibrium points is investigated to explore the intrinsic driving mechanisms of population interaction modes. It is shown that the system undergoes various bifurcations, including transcritical, saddle-node, Hopf and Bogdanov-Takens bifurcations. The numerical simulation results show that harvesting and fear effect can seriously affect the dynamic evolution trend and coexistence mode. Furthermore, it is particularly worth pointing out that harvesting not only drives changes in population coexistence mode, but also has a certain degree delay. Finally, it is anticipated that these research results will be beneficial for the vigorous development of predator-prey system.

Stability switches and chaos induced by delay in a reaction-diffusion nutrient-plankton model.

In this paper, we investigate a reaction-diffusion model incorporating dynamic variables for nutrient, phytoplankton, and zooplankton. Moreover, we account for the impact of time delay in the growth of phytoplankton following nutrient uptake. Our theoretical analysis reveals that the time delay can trigger the emergence of persistent oscillations in the model via a Hopf bifurcation. We also analytically track the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions. Our simulation results demonstrate stability switches occurring for the positive equilibrium with an increasing time lag. Furthermore, the model exhibits homogeneous periodic-2 and 3 solutions, as well as chaotic behaviour. These findings highlight that the presence of time delay in the phytoplankton growth can bring forth dynamical complexity to the nutrient-plankton system of aquatic habitats.

Investigation of a nutrient-plankton model with stochastic fluctuation and impulsive control.

In this paper, we investigate a stochastic nutrient-plankton model with impulsive control of the nutrient concentration and zooplankton population. Analytically, we find that the population size is nonnegative for a sufficiently long time. We derive some sufficient conditions for the existence of stable periodic oscillations, which indicate that the plankton populations will behave periodically. The numerical results show that the plankton system experiences a transition from extinction to the coexistence of species due to the emergence of impulsive control. Additionally, we observe that the nutrient pulse has a stronger relationship with phytoplankton growth than the zooplankton pulse. Although the frequency of impulsive control and appropriate environmental fluctuations can promote the coexistence of plankton populations, an excessive intensity of noise can result in the collapse of the entire ecosystem. Our findings may provide some insights into the relationships among nutrients, phytoplankton and zooplankton in a stochastic environment.

Dynamics of a harvested cyanobacteria-fish model with modified Holling type â £ functional response.

In this paper, considering the aggregation effect and Allee effect of cyanobacteria populations and the harvesting of both cyanobacteria and fish by human beings, a new cyanobacteria-fish model with two harvesting terms and a modified Holling type Ⅳ functional response function is proposed. The main purpose of this paper is to further elucidate the influence of harvesting terms on the dynamic behavior of a cyanobacteria-fish model. Critical conditions for the existence and stability of several interior equilibria are given. The economic equilibria and the maximum sustainable total yield problem are also studied. The model exhibits several bifurcations, such as transcritical bifurcation, saddle-node bifurcation, Hopf bifurcation and Bogdanov-Takens bifurcation. It is concluded from a biological perspective that the survival mode of cyanobacteria and fish can be determined by the harvesting terms. Finally, concrete examples of our model are given through numerical simulations to verify and enrich the theoretical results.

Dual characteristics of Bellamya aeruginosa encountering Microcystis aeruginosa: Algal control and toxin depuration.

The benthic gastropods Bellamya aeruginosa (B. aeruginosa) is ubiquitous in freshwater in China and neighboring countries with great edible value. It has been recognized as a potential manipulator to control harmful algal blooms due to its filtration on algal cells. In this study, the control effect of B. aeruginosa on toxic and non-toxic Microcystis aeruginosa (M. aeruginosa), and the accumulation and depuration of microcystins (MCs) in the snail were systematically explored. Results indicated that although toxic M. aeruginosa could protect itself via producing MCs, the introduction of B. aeruginosa could still effectively inhibit the algae with cell density below 1 × 106 cells/mL. Hepatopancreas was the primary target of MCs in all tissues of B. aeruginosa, presenting a maximum of 3089.60 ng/g DW when exposed to toxic M. aeruginosa of 1.0 × 107 cells/mL. The enrichment of MCs in other tissues following the order of digestive tract > gonad > mantle > muscle. Interestingly, snail could again excrete previously enriched MCs when transferred to non-toxic M. aeruginosa, giving rise to over 80% reduction of MCs in the body. After depuration, the estimated daily intake (EDI) of free MCs in intact individuals and the edible parts of B. aeruginosa were both lower than the tolerable daily intake (TDI). These results implicated that B. aeruginosa could control low density of M. aeruginosa in spring. Particularly, the snail could be perfectly safe to consume by purifying for a while after using as manipulator.

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.

Dynamics of a predator-prey model with strong Allee effect and nonconstant mortality rate.

In this paper, dynamics analysis for a predator-prey model with strong Allee effect and nonconstant mortality rate are taken into account. We systematically studied the existence and stability of the equilibria, and detailedly analyzed various bifurcations, including transcritical, saddle-node, Hopf and Bogdanov-Takens bifurcation. In addition, the theoretical results are verified by numerical simulations. The results indicate that when the mortality is large, the nonconstant death rate can be approximated to a constant value. However, it cannot be considered constant under small mortality rate conditions. Unlike the extinction of species for the constant mortality, the nonconstant mortality may result in the coexistence of prey and predator for the predator-prey model with Allee effect.

Dynamic analysis of a modified algae and fish model with aggregation and Allee effect.

In the paper, under the stress of aggregation and reproduction mechanism of algae, we proposed a modified algae and fish model with aggregation and Allee effect, its main purpose was to further ascertain the dynamic relationship between algae and fish. Several critical conditions were investigated to guarantee the existence and stabilization of all possible equilibrium points, and ensure that the model could undergo transcritical bifurcation, saddle-node bifurcation, Hopf bifurcation and B-T bifurcation. Numerical simulation results of related bifurcation dynamics were provided to verify the feasibility of theoretical derivation, and visually demonstrate the changing trend of the dynamic relationship. Our results generalized and improved some known results, and showed that the aggregation and Allee effect played a vital role in the dynamic relationship between algae and fish.

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

In this paper, in order to explore the inhibition mechanism of algicidal bacteria on algae, we constructed an aquatic amensalism model with non-selective harvesting and Allee effect. Mathematical works mainly gave some critical conditions to guarantee the existence and stability of equilibrium points, and derived some threshold conditions for saddle-node bifurcation and transcritical bifurcation. Numerical simulation works mainly revealed that non-selective harvesting played an important role in amensalism dynamic relationship. Meanwhile, we proposed some biological explanations for transcritical bifurcation and saddle-node bifurcation from the aspect of algicidal bacteria controlling algae. Finally, all these results were expected to be useful in studying dynamical behaviors of aquatic amensalism ecosystems and biological algae controlling technology.

Inhibitory effects of Prorocentrum donghaiense allelochemicals on Sargassum fusiformis zygotes probed by JIP-test based on fast chlorophyll fluorescence kinetics.

The macro- and microalgae have been found to inhibit the growth and photosynthesis of one another due to allelopathic interactions between them. Sargassum fusiformis is a common and commercially cultivated seaweed in coastal waters of the East China Sea (ECS) and usually encounters dense harmful algal blooms (HABs) formed by dinoflagellates during their sexual reproduction period. In the present study, the effects of Prorocentrum donghaiense lipophilic extracted allelochemicals on the growth and photosynthesis of S. fusiformis zygotes were probed by fast chlorophyll fluorescence rise kinetics and chlorophyll a transient analysis (JIP-test). It was found that exposure to the allelochemicals led to decreased chlorophyll a content and photosynthetic rates of the zygotes in comparison to the ones in the control. In addition, using the JIP-test, it was found that the inhibitory effects of allelochemicals on photosynthesis of the zygotes were mainly exerted on the electron transport within PSII. The decrease of photosynthetic parameters such as VJ, Mo, ϕPo, ϕo, ϕEo, PI, PTR, PET in the zygotes exposed to the allelochemicals all revealed that the obstruction of electron transport, and the dominant decrease in PET, both implied that inhibition on the dark reaction contributed to the highest photosynthetic reduction. In addition, some reaction centers (RCs) in the zygotes exposed to the allelocamicals were inactivated, which led to higher dissipation of excitation energy, as demonstrated by the significant enhancement of the photosynthetic parameter DIo/RC. All the results indicated that the lipophilic extracts contained the allelochemicals of P. donghaiense which could inhibit the growth and photosynthesis of S. fusiformis zygotes by damaging the electron acceptors and inactivating RCs, and finally block the electron transport.

Hopf bifurcation in an age-structured prey-predator model with Holling â ¢ response function.

In this paper, we propose a prey-predator model with age structure which is described by the mature period. The aim of this paper is to study how mature period affect the dynamics of interaction between prey and predator. The sufficient condition of the existence of non-negative steady state is derived. By using integrated semigroup theory, we obtain the characteristic equation, by which we find that the non-negative steady state will lose its stability via Hopf bifurcation induced by mature period, and the corresponding periodic solutions emerge. Additionally, some numerical simulations are provided to illustrate the results predicted by linear analysis. Especially, the numerical results indicate that both mature period and age can affect the amplitude and period of periodic solutions.

Dynamics induced by environmental stochasticity in a phytoplankton-zooplankton system with toxic phytoplankton.

Environmental stochasticity and toxin-producing phytoplankton (TPP) are the key factors that affect the aquatic ecosystems. To investigate the effects of environmental stochasticity and TPP on the dynamics of plankton populations, a stochastic phytoplankton-zooplankton system with two TPP is studied theoretically and numerically in this paper. Theoretically, we first prove that the system possesses a unique and global positive solution with positive initial values, and then derive some sufficient conditions guaranteeing the extinction and persistence in the mean of the system. Significantly, it is shown that the system has a stationary distribution when toxin liberation rate reaches some a critical value. Additionally, numerical analysis shows that the white noise can affect the survival of plankton populations directly. Furthermore, it has been observed that the increasing one toxin liberation rate can increase the survival chance of phytoplankton and reduce the biomass of zooplankton, but the combined effects of two liberation rates on the changes in plankton populations are stronger than that of controlling any one of the two TPP.

Combined process of bio-contact oxidation-constructed wetland for blackwater treatment.

In this study, a combined process of bio-contact oxidation and constructed wetland for blackwater treatment was assessed. The effects of hydraulic retention time and particle size on treatment performance were systematically studied. Additionally, microbial communities in the combined process were characterized. The results show that the removal efficiency of COD, TN, NH4+-N, and TP under optimum conditions in this study were 81.6%, 56.1%, 42.2%, and 73.7%, respectively. The maximum nitrogen removal rate reached 16.5 g m-2 d-1 (3 d). N and P removed via direct plant absorption accounted for only 19.7% and 16.1% of the total system, respectively. Plants play a crucial role in the microbial community of constructed wetlands and influence the overall performance of the system. The biofilm on roots favored aerobic and heterotrophic bacteria such as the aerobic denitrification microorganisms of Pelagibacterium, Halomonas, and Zoogloea. Overall, the combined process is a suitable technique for the treatment of blackwater.

Bifurcation and patterns induced by flow in a prey-predator system with Beddington-DeAngelis functional response.

In this paper, a prey-predator system described by a couple of advection-reaction-diffusion equations is studied theoretically and numerically, where the migrations of both prey and predator are considered and depicted by the unidirectional flow (advection term). To investigate the effect of population migration, especially the relative migration between prey and predator, on the population dynamics and spatial distribution of population, we systematically study the bifurcation and pattern dynamics of a prey-predator system. Theoretically, we derive the conditions for instability induced by flow, where neither Turing instability nor Hopf instability occurs. Most importantly, linear analysis indicates the instability induced by flow depends only on the relative flow velocity. Specifically, when the relative flow velocity is zero, the instability induced by flow does not occur. Moreover, the diffusion-driven patterns at the same flow velocity may not be stationary because of the contribution of flow. Numerical bifurcation analyses are consistent with the analytical results and show that the patterns induced by flow may be traveling waves with different wavelengths, amplitudes, and speeds, which are illustrated by numerical simulations.

Cell density-dependent suppression on the development and photosynthetic activities of Sargassum fusiformis embryos by dinoflagellate Karenia mikimotoi.

Lots of research has demonstrated that macroalgae can strongly inhibit the growth of harmful algal bloom (HAB) species in general. However, the effects of HABs or HAB-forming species on macrophytes are still largely uncharacterized until now. In the present study, the effects of the dinoflagellate Karenia mikimotoi cell density gradient, live cell suspension (LC), ruptured cell suspension (RC) as well as the cell-free supernatant (FC) of K. mikimotoi at 1000 µg Chla l-1 (~1.0 × 105 cells ml-1) on the development and photosynthesis of Sargassum fusiforme embryos were investigated in a series of laboratory experiments. The results showed that co-cultivation with K. mikimotoi at 500 µg Chla l-1(~5.0 × 104 cells ml-1) and higher cell densities significantly (P<0.05) inhibited the development, pigment content and photosynthetic activities of the embryos. In addition, the inhibitory effects increased with increased cell densities and prolonged exposure time. Compared to the embryos cultured with the F/2 medium (Control), exposure to LC, RC and FC of K. mikimotoi at 1000 µg Chla l-1for 2 weeks all led to decreased relative growth rate (RGR), chlorophyll (Chl) a content, carotenoids (Car) content and photosynthetic activities of the embryos, with LC and RC exhibiting the maximal and the minimal suppression. The dominant inhibitory effects of FC on the embryos indicated that the suppression was mainly caused by the allelochemicals, while the slightest inhibitory effects of RC on the embryos suggested that some intracellular growth-promoting substances were synchronously released when K. mikimotoi cells lyzed. In addition, the most severe growth suppression of embryos by LC indicated that intact cell contact by K. mikimotoi probably also contributed to the inhibitory effects. These results indicated that a dense HAB formed by K. mikimotoi could seriously suppress the development and photosynthesis of S. fusiforme embryos and eventually reduce the seedlings stock.

Delay-induced instability in a nutrient-phytoplankton system with flow.

In this paper, a nutrient-phytoplankton system described by a couple of advection-diffusion-reaction equations with delay was studied analytically and numerically. The aim of this research was to provide an understanding of the impact of delay on instability. Significantly, delay cannot only induce instability, but can also promote the formation of spatial pattern via a Turing-like instability. In addition, the theoretical analysis indicates that the flow (advection term) may lead to instability when the delay term exists. By comparison, diffusion cannot result in Turing instability when flow does not exist. Results of numerical simulation were consistent with the analytical results.