Dynamic Analysis of a Phytoplankton-Fish Model with Biological and Artificial Control

We investigate a nonlinear model of the interaction between phytoplankton and fish, which uses a pair of semicontinuous systems with biological and artificial control. First, the existence of an order-1 periodic solution to the system is analyzed using a Poincaré map and a geometric method. The stability conditions of the order-1 periodic solution are obtained by a theoretical mathematical analysis. Furthermore, based on previous analysis, we investigate the bifurcation in the order-1 periodic solution and prove that the order-1 periodic solution breaks up an order-1 periodic solution at least. In addition, the transcritical bifurcation of the system is described. Finally, we provide a series of numerical results that illustrate the feasibility of the theoretical results. Based on the theoretical and numerical results, we analyzed the feasibility of biological and artificial control, which showed that biological and artificial methods can control phytoplankton blooms. These results are expected to be useful for the study of phytoplankton dynamics in aquatic ecosystems

Stability and Hopf Bifurcation Analysis of a Nutrient-Phytoplankton Model with Delay Effect

A delay differential system is investigated based on a previously proposed nutrient-phytoplankton model. The time delay is regarded as a bifurcation parameter. Our aim is to determine how the time delay affects the system. First, we study the existence and local stability of two equilibria using the characteristic equation and identify the condition where a Hopf bifurcation can occur. Second, the formulae that determine the direction of the Hopf bifurcation and the stability of periodic solutions are obtained using the normal form and the center manifold theory. Furthermore, our main results are illustrated using numerical simulations

Nonlinear Dynamics of a Nutrient-Plankton Model

We investigated a nonlinear model of the interaction between nutrients and plankton, which was addressed using a pair of reaction-advection-diffusion equations. Based on numerical analysis, we studied a model without diffusion and sinking terms, and we found that the phytoplankton density (a stable state) increased with the increase of nutrient density. We analyzed the model using a linear analysis technique and found that the sinking of phytoplankton could affect the system. If the sinking velocity exceeded a certain critical value, the stable state became unstable and the wavelength of phytoplankton increased with the increase of sinking velocity. Furthermore, band patterns were also produced by our model, which was affected by the diffusion and sinking of phytoplankton. Thus, the change in the diffusion and sinking of phytoplankton led to different spatial distributions of phytoplankton. All of these results are expected to be useful in the study of plankton dynamics in aquatic ecosystems

Fast determination of polybrominated diphenyl ethers residues in milk by dispersive solid phase extraction and isotope labeled internal standard-gas chromatography-tandem mass spectrometry

Objective A 13C isotope labeled internal standard-gas chromatography-tandem mass spectrometric (GC-MS/MS) with dispersive solid phase extraction (d-SPE) method was developed for the simultaneous determination of 7 polybrominated diphenyl ethers (PBDEs) residues in milk. Methods After adding13C12 isotope internal standard and extracted with 1% acetic acid acetonitrile, purified with the new Z-Sep+C18 dispersive agent, the analytes in the sample solutions were seperated by DB-5 column (30 m×0.25 mm, 0.25 μm). Operated by electron impact ion source (EI) with multiple reactions monitoring (MRM) mode, the samples were analyzed by gas chromatography-tandem mass spectrometer. The quantifications were performed by the isotope internal standard method with matrix-matched calibration standards. Results Good linearity was obtained for 7 PBDEs in the concentration range of 0.500-100 ng/mL with correlation coefficients (r) above 0.999. Recoveries for 7 PBDEs at three spiked levels of 0.1, 1.0, and 10 μg/kg were in the range of 89.7%-102.9% with relative standard deviations (RSDs, n = 6) of 3.8%-8.3%. The limits of detection and the limits of quantification were in the ranges of 2.4-9.8 and 7.5-30 ng/kg, respectively. Conclusion The established method was simple, efficient and sensitive, and could be applied in the determination of 7 PBDEs in milk

Dynamic Analysis of a Delayed Reaction-Diffusion Predator-Prey System with Modified Holling-Tanner Functional Response

A predator-prey model with modified Holling-Tanner functional response and time delays is considered. By regarding the delays as bifurcation parameters, the local and global asymptotic stability of the positive equilibrium are investigated. The system has been found to undergo a Hopf bifurcation at the positive equilibrium when the delays cross through a sequence of critical values. In addition, the direction of the Hopf bifurcation and the stability of bifurcated periodic solutions are also studied, and an explicit algorithm is obtained by applying normal form theory and the center manifold theorem. The main results are illustrated by numerical simulations

Stability and Dynamical Analysis of a Biological System

This study considers the spatiotemporal dynamics of a reaction-diffusion phytoplankton-zooplankton system with a double Allee effect on prey under a homogeneous boundary condition. The qualitative properties are analyzed, including the local stability of all equilibria and the global asymptotic property of the unique positive equilibrium. We also discuss the Hopf bifurcation and the steady state bifurcation of the system. These results are expected to help understand the complexity of the Allee effect and the interaction between phytoplankton and zooplankton

Research Progress of Milk-derived Blood Pressure-lowering Peptides

Hypertension is a "silent killer" that threatens human health. Milk-derived antihypertensive peptides with antihypertensive activity are prepared from milk protein by enzymatic hydrolysis or fermentation. Recent years, milk-derived antihypertensive peptides have been regarded as a natural and relatively safe bioactive peptide, which have attracted increasing attention due to their high biological activity, low toxicity, easy metabolism and good antihypertensive effect. And milk-derived antihypertensive peptides have been gradually applied to health care products, functional foods and other fields. In this paper, the research progress in the sources (chemically synthesized and natural food sources) and preparation methods (digestibility in vitro and microbial fermentation). This paper summarizes the separation and purification, and structure-activity relationship of milk-derived antihypertensive peptides is reviewed, and the future development prospects for food and clinical applications are outlined, which will provide reference for promoting the development of antihypertensive peptide products in China

The antioxidative effect of electro-acupuncture in a mouse model of Parkinson's disease.

Accumulating evidence indicates that oxidative stress plays a critical role in Parkinson's disease (PD). Our previous work has shown that 100 Hz electro-acupuncture (EA) stimulation at ZUSANLI (ST36) and SANYINJIAO (SP6) protects neurons in the substantia nigra pars compacta from 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP) toxicity in male C57BL/6 mice, a model of PD. In the present study we administered 100 Hz EA stimulation at the two acupoints to MPTP-lesioned mice for 12 sessions starting from the day prior to the first MPTP injection. We found that in the striatum of MPTP treated mice 100 Hz EA stimulation effectively inhibited the production of hydrogen peroxide and malonaldehyde, and increased glutathione concentration and total superoxide dismutase activity through biochemical methods. However, it decreased glutathione peroxidase activity via biochemical analysis and did not affect the level of 1-methyl-4-phenylpyridinium in the striatum revealed by high performance liquid chromatography with ultraviolet detection. These data suggest that 100 Hz EA stimulation at ST36 and SP6 has antioxidative effects in the MPTP model of PD. This data, along with our previous work, indicates that 100 Hz EA stimulation at ST36 and SP6 protects the nigrostriatal system by multiple mechanisms including antioxidation and antiapoptosis, and suggests that EA stimulation is a promising therapy for treating PD